메뉴 건너뛰기




Volumn 195, Issue 1, 2009, Pages 25-73

Well-posedness and regularity for the elasticity equation with mixed boundary conditions on polyhedral domains and domains with cracks

Author keywords

[No Author keywords available]

Indexed keywords


EID: 70350666471     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0180-y     Document Type: Article
Times cited : (72)

References (97)
  • 1
    • 0003924563 scopus 로고
    • Prepared for publication by Frank Jones, B. Jr. with the assistance of George W. Batten, Jr. van Nostrand Mathematical Studies, No. 2. D. van Nostrand Co., Inc., Princeton, London
    • Agmon, S.: Lectures on elliptic boundary value problems. Prepared for publication by Frank Jones, B. Jr. with the assistance of George W. Batten, Jr. van Nostrand Mathematical Studies, No. 2. D. van Nostrand Co., Inc., Princeton, London, 1965.
    • (1965) Lectures on Elliptic Boundary Value Problems
    • Agmon, S.1
  • 2
    • 84980080664 scopus 로고
    • Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm
    • Agmon S., Douglis A., Nirenberg L.: Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. II. Comm. Pure Appl. Math. 17, 35-92 (1964).
    • (1964) Pure Appl. Math. , vol.17 , pp. 35-92
    • Agmon, S.1    Douglis, A.2    Nirenberg, L.3
  • 3
    • 33845468329 scopus 로고    scopus 로고
    • Sobolev spaces on Lie manifolds and regularity for polyhedral domains
    • (electronic)
    • Ammann, B., Ionescu, A., Nistor, V. Sobolev spaces on Lie manifolds and regularity for polyhedral domains. Doc. Math., 11, 161-206 (electronic) 2006.
    • (2006) Doc. Math. , vol.11 , pp. 161-206
    • Ammann, B.1    Ionescu, A.2    Nistor, V.3
  • 4
    • 34447118218 scopus 로고    scopus 로고
    • Weighted sobolev spaces and regularity for polyhedral domains
    • Ammann B., Nistor V.: Weighted sobolev spaces and regularity for polyhedral domains. Comput. Methods Appl. Mech. Eng. 196, 3650-3659 (2007).
    • (2007) Comput. Methods Appl. Mech. Eng. , vol.196 , pp. 3650-3659
    • Ammann, B.1    Nistor, V.2
  • 5
    • 0032046927 scopus 로고    scopus 로고
    • The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges
    • Apel T., Nicaise S.: The finite element method with anisotropic mesh grading for elliptic problems in domains with corners and edges. Math. Methods Appl. Sci. 21(6), 519-549 (1998).
    • (1998) Math. Methods Appl. Sci. , vol.21 , Issue.6 , pp. 519-549
    • Apel, T.1    Nicaise, S.2
  • 6
    • 0036879773 scopus 로고    scopus 로고
    • Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes
    • 2002
    • Apel, T., Sändig, A.-M., Solov′ev, S.: Computation of 3D vertex singularities for linear elasticity: Error estimates for a finite element method on graded meshes. M2AN Math. Model. Numer. Anal., 36(6), 1043-1070 (2003), 2002.
    • (2003) M2AN Math. Model. Numer. Anal. , vol.36 , Issue.6 , pp. 1043-1070
    • Apel, T.1    Sändig, A.-M.2    Solov′ev, S.3
  • 7
    • 0041073868 scopus 로고    scopus 로고
    • Multigrid preconditioning in H(div) on non-convex polygons
    • Arnold D., Falk R., Winther R.: Multigrid preconditioning in H(div) on non-convex polygons. Comput. Appl. Math. 17(3), 303-315 (1998).
    • (1998) Comput. Appl. Math. , vol.17 , Issue.3 , pp. 303-315
    • Arnold, D.1    Falk, R.2    Winther, R.3
  • 8
    • 0001676787 scopus 로고
    • Espaces de Sobolev sur les variétés riemanniennes
    • Aubin, T.: Espaces de Sobolev sur les variétés riemanniennes. Bull. Sci. Math. (2), 100(2), 149-173 (1976).
    • (1976) Bull. Sci. Math. (2) , vol.100 , Issue.2 , pp. 149-173
    • Aubin, T.1
  • 9
    • 0033114779 scopus 로고    scopus 로고
    • On the best Sobolev inequality
    • Aubin, T., Li, Y.Y.: On the best Sobolev inequality. J. Math. Pures Appl. (9), 78(4), 353-387 (1999).
    • (1999) J. Math. Pures Appl. (9) , vol.78 , Issue.4 , pp. 353-387
    • Aubin, T.1    Li, Y.Y.2
  • 10
    • 0015077617 scopus 로고
    • The rate of convergence for the finite element method
    • Babuška I.: The rate of convergence for the finite element method. SIAM J. Numer. Anal. 8, 304-315 (1971).
    • (1971) SIAM J. Numer. Anal. , vol.8 , pp. 304-315
    • Babuška, I.1
  • 11
    • 0002679574 scopus 로고
    • Survey lectures on the mathematical foundations of the finite element method
    • Proceedings of Symposium, University of Maryland, Baltimore, pp. 1-359. Academic Press, New York, (With the collaboration of G. Fix and R. Kellogg)
    • Babuška, I., Aziz, A.K.: Survey lectures on the mathematical foundations of the finite element method. In: The mathematical foundations of the finite element method with applications to partial differential equations. Proceedings of Symposium, University of Maryland, Baltimore, pp. 1-359. Academic Press, New York, 1972 (With the collaboration of G. Fix and R. Kellogg).
    • (1972) The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations
    • Babuška, I.1    Aziz, A.K.2
  • 12
    • 34447128246 scopus 로고
    • Optimization of numerical processes
    • Babuška I., Sobolev S.L.: Optimization of numerical processes. Appl. Math. 10, 96-129 (1965).
    • (1965) Appl. Math. , vol.10 , pp. 96-129
    • Babuška, I.1    Sobolev, S.L.2
  • 15
    • 29044437906 scopus 로고    scopus 로고
    • Improving the rate of convergence of high-order finite elements on polyhedra. I. A priori estimates
    • Bacuta C., Nistor V., Zikatanov L.T.: Improving the rate of convergence of high-order finite elements on polyhedra. I. A priori estimates. Numer. Funct. Anal. Optim. 26(6), 613-639 (2005).
    • (2005) Numer. Funct. Anal. Optim. , vol.26 , Issue.6 , pp. 613-639
    • Bacuta, C.1    Nistor, V.2    Zikatanov, L.T.3
  • 17
    • 0037354898 scopus 로고    scopus 로고
    • A proof of the inf-sup condition for the Stokes equations on Lipschitz domains
    • Dedicated to Jim Douglas, Jr. on the occasion of his 75th birthday
    • Bramble, J.H.: A proof of the inf-sup condition for the Stokes equations on Lipschitz domains. Math. Models Methods Appl. Sci., 13(3), 361-371, 2003. Dedicated to Jim Douglas, Jr. on the occasion of his 75th birthday.
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , Issue.3 , pp. 361-371
    • Bramble, J.H.1
  • 18
    • 0345325406 scopus 로고    scopus 로고
    • The mathematical theory of finite element methods
    • Springer, New York, 2nd edn
    • Brenner, S., Scott, R.: The mathematical theory of finite element methods, vol. 15, Texts in Applied Mathematics. Springer, New York, 2nd edn, 2002.
    • (2002) Texts in Applied Mathematics , vol.15
    • Brenner, S.1    Scott, R.2
  • 19
    • 17444419688 scopus 로고    scopus 로고
    • Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps
    • Bǎcuţǎ C., Nistor V., Zikatanov L.: Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps. Numer. Math. 100, 165-184 (2005).
    • (2005) Numer. Math. , vol.100 , pp. 165-184
    • Bǎcuţǎ, C.1    Nistor, V.2    Zikatanov, L.3
  • 20
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • Cheeger M., Gromov J., Taylor M.: Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differ. Geom. 17(1), 15-53 (1982).
    • (1982) J. Differ. Geom. , vol.17 , Issue.1 , pp. 15-53
    • Cheeger, M.1    Gromov, J.2    Taylor, M.3
  • 21
    • 0036627721 scopus 로고    scopus 로고
    • A Riemannian version of Korn's inequality
    • Chen W., Jost J.: A Riemannian version of Korn's inequality. Calc. Var. Partial Differ. Equ. 14(4), 517-530 (2002).
    • (2002) Calc. Var. Partial Differ. Equ. , vol.14 , Issue.4 , pp. 517-530
    • Chen, W.1    Jost, J.2
  • 22
    • 0038582197 scopus 로고    scopus 로고
    • Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotic
    • Chkadua O., Duduchava R.: Pseudodifferential equations on manifolds with boundary: Fredholm property and asymptotic. Math. Nachr. 222, 79-139 (2001).
    • (2001) Math. Nachr. , vol.222 , pp. 79-139
    • Chkadua, O.1    Duduchava, R.2
  • 23
    • 34250286856 scopus 로고
    • Boundary integral operators on curved polygons
    • Costabel M.: Boundary integral operators on curved polygons. Ann. Math. Pura Appl. 4(133), 305-326 (1983).
    • (1983) Ann. Math. Pura Appl. , vol.4 , Issue.133 , pp. 305-326
    • Costabel, M.1
  • 24
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: Elementary results
    • Costabel M.: Boundary integral operators on Lipschitz domains: Elementary results. SIAM J. Math. Anal. 19(3), 613-626 (1988).
    • (1988) SIAM J. Math. Anal. , vol.19 , Issue.3 , pp. 613-626
    • Costabel, M.1
  • 25
    • 0002534607 scopus 로고
    • Computation of corner singularities in linear elasticity. In: Boundary value problems and integral equations in nonsmooth domains (Luminy, 1993)
    • Dekker, New York
    • Costabel, M., Dauge, M.: Computation of corner singularities in linear elasticity. In: Boundary value problems and integral equations in nonsmooth domains (Luminy, 1993), vol. 167, Lecture Notes in Pure and Appl. Math., pp. 59-68. Dekker, New York, 1995.
    • (1995) Lecture Notes in Pure and Appl. Math. , vol.167 , pp. 59-68
    • Costabel, M.1    Dauge, M.2
  • 26
    • 0036069797 scopus 로고    scopus 로고
    • Crack singularities for general elliptic systems
    • Costabel M., Dauge M.: Crack singularities for general elliptic systems. Math. Nachr. 235, 29-49 (2002).
    • (2002) Math. Nachr. , vol.235 , pp. 29-49
    • Costabel, M.1    Dauge, M.2
  • 27
    • 34447130335 scopus 로고    scopus 로고
    • Corner singularities of Maxwell interface and eddy current problems
    • Oper. Theory Adv. Appl., Birkhäuser, Basel
    • Costabel, M., Dauge, M., Nicaise, S.: Corner singularities of Maxwell interface and eddy current problems. In: Operator theoretical methods and applications to mathematical physics, vol. 147, Oper. Theory Adv. Appl., pp. 241-256. Birkhäuser, Basel, 2004.
    • (2004) Operator Theoretical Methods and Applications to Mathematical Physics , vol.147 , pp. 241-256
    • Costabel, M.1    Dauge, M.2    Nicaise, S.3
  • 28
    • 0036681310 scopus 로고    scopus 로고
    • Steady growth of a crack with a rate and temperature sensitive cohesive zone
    • Costanzo F., Walton J.: Steady growth of a crack with a rate and temperature sensitive cohesive zone. J. Mech. Phys. Solids 50, 1649-1679 (2002).
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 1649-1679
    • Costanzo, F.1    Walton, J.2
  • 29
    • 0003573037 scopus 로고
    • of Lecture Notes in Mathematics Springer, Berlin, (Smoothness and asymptotics of solutions)
    • Dauge, M.: Elliptic boundary value problems on corner domains, vol. 1341 of Lecture Notes in Mathematics. Springer, Berlin, 1988 (Smoothness and asymptotics of solutions).
    • (1988) Elliptic Boundary Value Problems on Corner Domains , vol.1341
    • Dauge, M.1
  • 30
    • 0035808194 scopus 로고    scopus 로고
    • A generalized finite element method for the simulation of three-dimensional dynamic crack propagation
    • Duarte A., Hamzeh O., Liszka T., Tworzydlo W.: A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Comput. Methods Appl. Mech. Eng. 190, 2227-2262 (2001).
    • (2001) Comput. Methods Appl. Mech. Eng. , vol.190 , pp. 2227-2262
    • Duarte, A.1    Hamzeh, O.2    Liszka, T.3    Tworzydlo, W.4
  • 31
    • 0005739419 scopus 로고    scopus 로고
    • Mixed crack type problem in anisotropic elasticity
    • Duduchava R., Natroshvili D.: Mixed crack type problem in anisotropic elasticity. Math. Nachr. 191, 83-107 (1998).
    • (1998) Math. Nachr. , vol.191 , pp. 83-107
    • Duduchava, R.1    Natroshvili, D.2
  • 32
    • 33645519531 scopus 로고    scopus 로고
    • Singular integral equations in special weighted spaces
    • Duduchava R., Speck F.-O.: Singular integral equations in special weighted spaces. Georgian. Math. J. 7(4), 633-642 (2000).
    • (2000) Georgian. Math. J. , vol.7 , Issue.4 , pp. 633-642
    • Duduchava, R.1    Speck, F.-O.2
  • 33
    • 0012869632 scopus 로고
    • Inequalities in mechanics and physics
    • Translated from the French by C. W. John, Springer, Berlin
    • Duvaut, G., Lions, J.-L.: Inequalities in mechanics and physics. Translated from the French by C. W. John, Grundlehren der Mathematischen Wissenschaften, 219. Springer, Berlin, 1976.
    • (1976) Grundlehren der Mathematischen Wissenschaften , vol.219
    • Duvaut, G.1    Lions, J.-L.2
  • 34
    • 0003228130 scopus 로고    scopus 로고
    • Partial differential equations
    • American Mathematical Society, Providence
    • Evans, L.C.: Partial differential equations, vol. 19, Graduate Studies in Mathematics. American Mathematical Society, Providence, 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 35
    • 84966201698 scopus 로고
    • Nonconforming finite element methods for the equations of linear elasticity
    • Falk R.: Nonconforming finite element methods for the equations of linear elasticity. Math. Comp. 57(196), 529-550 (1991).
    • (1991) Math. Comp. , vol.57 , Issue.196 , pp. 529-550
    • Falk, R.1
  • 36
    • 84968484655 scopus 로고
    • Remarks on mixed finite element methods for problems with rough coefficients
    • Falk R., Osborn J.: Remarks on mixed finite element methods for problems with rough coefficients. Math. Comp. 62(205), 1-19 (1994).
    • (1994) Math. Comp. , vol.62 , Issue.205 , pp. 1-19
    • Falk, R.1    Osborn, J.2
  • 39
    • 0000606420 scopus 로고
    • On the boundary-value problems of the theory of elasticity and Korn's inequality
    • Friedrichs, K.O.: On the boundary-value problems of the theory of elasticity and Korn's inequality. Ann. Math. (2), 48, 441-471 (1947).
    • (1947) Ann. Math. (2) , vol.48 , pp. 441-471
    • Friedrichs, K.O.1
  • 40
    • 0036384329 scopus 로고    scopus 로고
    • A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity
    • Friesecke G., James R., Müller S.: A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity. Comm. Pure Appl. Math. 55(11), 1461-1506 (2002).
    • (2002) Comm. Pure Appl. Math. , vol.55 , Issue.11 , pp. 1461-1506
    • Friesecke, G.1    James, R.2    Müller, S.3
  • 41
    • 0003320921 scopus 로고
    • Elliptic problems in nonsmooth domains
    • Pitman (Advanced Publishing Program), Boston
    • Grisvard, P.: Elliptic problems in nonsmooth domains, vol. 24, Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, 1985.
    • (1985) Monographs and Studies in Mathematics , vol.24
    • Grisvard, P.1
  • 42
    • 0000658992 scopus 로고
    • Singularités en elasticité
    • Grisvard P.: Singularités en elasticité. Arch. Ration. Mech. Anal. 107(2), 157-180 (1989).
    • (1989) Arch. Ration. Mech. Anal. , vol.107 , Issue.2 , pp. 157-180
    • Grisvard, P.1
  • 44
    • 0004279470 scopus 로고
    • Springer Series in Computational Mathematics, Berlin: Springer
    • Hackbusch W.: Multigrid methods and applications, vol. 4, Springer Series in Computational Mathematics. Springer, Berlin (1985).
    • (1985) Multigrid Methods and Applications , vol.4
    • Hackbusch, W.1
  • 45
    • 29444452747 scopus 로고    scopus 로고
    • Harmonic forms on manifolds with edges
    • Hunsicker, E., Mazzeo, R.: Harmonic forms on manifolds with edges. Int. Math. Res. Not., 2005(52), 3229-3272.
    • Int. Math. Res. Not. , vol.2005 , Issue.52 , pp. 3229-3272
    • Hunsicker, E.1    Mazzeo, R.2
  • 46
    • 84966201593 scopus 로고
    • The Neumann problem on Lipschitz domains
    • Jerison D., Kenig C.: The Neumann problem on Lipschitz domains. Bull. Am. Math. Soc. (N.S.) 4(2), 203-207 (1981).
    • (1981) Bull. Am. Math. Soc. (N.S.) , vol.4 , Issue.2 , pp. 203-207
    • Jerison, D.1    Kenig, C.2
  • 47
    • 0000271720 scopus 로고
    • The inhomogeneous Dirichlet problem in Lipschitz domains
    • Jerison D., Kenig C.: The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130(1), 161-219 (1995).
    • (1995) J. Funct. Anal. , vol.130 , Issue.1 , pp. 161-219
    • Jerison, D.1    Kenig, C.2
  • 48
    • 0002814972 scopus 로고
    • Boundary value problems on Lipschitz domains. Studies in partial differential equations
    • Math. Assoc. America, Washington, DC
    • Jerison, D.S., Kenig, C.E.: Boundary value problems on Lipschitz domains. Studies in partial differential equations, vol. 23, MAA Stud. Math., pp. 1-68. Math. Assoc. America, Washington, DC, 1982.
    • (1982) MAA Stud. Math. , vol.23 , pp. 1-68
    • Jerison, D.S.1    Kenig, C.E.2
  • 51
    • 0000946498 scopus 로고
    • Recent progress on boundary value problems on Lipschitz domains
    • Proceedings of Symposium in Pure Mathematics. American Mathematical Society, Providence
    • Kenig, C.: Recent progress on boundary value problems on Lipschitz domains. Pseudodifferential operators and applications (Notre Dame, Ind., 1984), vol. 43, Proceedings of Symposium in Pure Mathematics, pp. 175-205. American Mathematical Society, Providence, 1985.
    • (1985) Pseudodifferential Operators and Applications (Notre Dame, Ind., 1984) , vol.43 , pp. 175-205
    • Kenig, C.1
  • 52
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic equations in domains with conical or angular points
    • Kondrat′ev V.A.: Boundary value problems for elliptic equations in domains with conical or angular points. Transl. Moscow Math. Soc. 16, 227-313 (1967).
    • (1967) Transl. Moscow Math. Soc. , vol.16 , pp. 227-313
    • Kondratev, V.A.1
  • 53
    • 0003325353 scopus 로고    scopus 로고
    • Spectral problems associated with corner singularities of solutions to elliptic equations
    • American Mathematical Society, Providence
    • Kozlov, V., Maz′ya, V., Rossmann, J.: Spectral problems associated with corner singularities of solutions to elliptic equations, vol. 85, Mathematical Surveys and Monographs. American Mathematical Society, Providence, 2001.
    • (2001) Mathematical Surveys and Monographs , vol.85
    • Kozlov, V.1    Maz′ya, V.2    Rossmann, J.3
  • 54
    • 84975960884 scopus 로고
    • On stress singularities near the boundary of a polygonal crack
    • Kozlov V.A., Maz′ya V.G.: On stress singularities near the boundary of a polygonal crack. Proc. R. Soc. Edinburgh Sect. A 117(1-2), 31-37 (1991).
    • (1991) Proc. R. Soc. Edinburgh Sect. A , vol.117 , Issue.1-2 , pp. 31-37
    • Kozlov, V.A.1    Mazya, V.G.2
  • 55
    • 84932346062 scopus 로고
    • On the degree of convergence of discrete approximations for the solutions of the Dirichlet problem
    • Laasonen, P.: On the degree of convergence of discrete approximations for the solutions of the Dirichlet problem. Ann. Acad. Sci. Fenn. Ser. A. I. 1957(246), 19 (1957).
    • (1957) Ann. Acad. Sci. Fenn. Ser. A. I. , vol.1957 , Issue.246 , pp. 19
    • Laasonen, P.1
  • 56
    • 0001303691 scopus 로고
    • Pseudodifferential operators of Mellin type
    • Lewis J., Parenti C.: Pseudodifferential operators of Mellin type. Comm. Partial Differ. Equ. 8(5), 477-544 (1983).
    • (1983) Comm. Partial Differ. Equ. , vol.8 , Issue.5 , pp. 477-544
    • Lewis, J.1    Parenti, C.2
  • 57
    • 84966233940 scopus 로고
    • Layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains
    • Lewis J.E.: Layer potentials for elastostatics and hydrostatics in curvilinear polygonal domains. Trans. Am. Math. Soc. 320(1), 53-76 (1990).
    • (1990) Trans. Am. Math. Soc. , vol.320 , Issue.1 , pp. 53-76
    • Lewis, J.E.1
  • 59
    • 9344241343 scopus 로고
    • Problèmes aux limites non homogènes et applications
    • Dunod, Paris
    • Lions, J.-L., Magenes, E.: Problèmes aux limites non homogènes et applications, vol. 1. Travaux et Recherches Mathématiques, No. 17. Dunod, Paris, 1968.
    • (1968) Travaux et Recherches Mathématiques , vol.1 , Issue.17
    • Lions, J.-L.1    Magenes, E.2
  • 61
    • 0003379140 scopus 로고
    • Elliptic boundary value problems on manifolds with singularities
    • Spectral theory, boundary value problems (Russian), 203. Izdat. Leningrad. Univ., Leningrad
    • Maz'eja, V.G., Plamenevskiǐ, B.A.: Elliptic boundary value problems on manifolds with singularities. In: Problems in mathematical analysis, No. 6: Spectral theory, boundary value problems (Russian), pp. 85-142, 203. Izdat. Leningrad. Univ., Leningrad, 1977.
    • (1977) Problems in Mathematical Analysis , Issue.6 , pp. 85-142
    • Maz'eja, V.G.1    Plamenevskiǐ, B.A.2
  • 62
    • 70350686836 scopus 로고
    • Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten. I
    • Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs]. Akademie-Verlag, Berlin. Störungen isolierter Randsingularitäten. [Perturbations of isolated boundary singularities]
    • Mazja, W.G., Nazarow, S.A., Plamenewski, B.A.: Asymptotische Theorie elliptischer Randwertaufgaben in singulär gestörten Gebieten. I, vol. 82, Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs]. Akademie-Verlag, Berlin, 1991. Störungen isolierter Randsingularitäten. [Perturbations of isolated boundary singularities].
    • (1991) Mathematische Lehrbücher und Monographien, II , vol.82
    • Mazja, W.G.1    Nazarow, S.A.2    Plamenewski, B.A.3
  • 63
    • 21144436774 scopus 로고    scopus 로고
    • p estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains
    • p estimates of solutions to boundary value problems for second order elliptic systems in polyhedral domains. ZAMM Z. Angew. Math. Mech. 83(7), 435-467 (2003).
    • (2003) ZAMM Z. Angew. Math. Mech. , vol.83 , Issue.7 , pp. 435-467
    • Maz'ya, V.1    Roßmann, J.2
  • 64
    • 84936145603 scopus 로고
    • Elliptic theory of differential edge operators. I. Commun
    • Mazzeo R.: Elliptic theory of differential edge operators. I. Commun. Partial Differ. Equ. 16(10), 1615-1664 (1991).
    • (1991) Partial Differ. Equ. , vol.16 , Issue.10 , pp. 1615-1664
    • Mazzeo, R.1
  • 68
    • 0035285749 scopus 로고    scopus 로고
    • Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds
    • Mitrea, D., Mitrea, M., Taylor, M.: Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds. Mem. Am. Math. Soc. 150(713), x+120 (2001).
    • (2001) Mem. Am. Math. Soc. , vol.150 , Issue.713
    • Mitrea, D.1    Mitrea, M.2    Taylor, M.3
  • 69
    • 37949040065 scopus 로고    scopus 로고
    • On the traction problem for the Lamé system on curvilinear polygons.J. Integral Equ
    • Mitrea I.: On the traction problem for the Lamé system on curvilinear polygons.J. Integral Equ. Appl. 16(2), 175-219 (2004).
    • (2004) Appl. , vol.16 , Issue.2 , pp. 175-219
    • Mitrea, I.1
  • 70
    • 37349060380 scopus 로고    scopus 로고
    • The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains
    • (electronic)
    • Mitrea, I., Mitrea, M.: The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains. Trans. Am. Math. Soc. 359(9), 4143-4182 (electronic), 2007.
    • (2007) Trans. Am. Math. Soc. , vol.359 , Issue.9 , pp. 4143-4182
    • Mitrea, I.1    Mitrea, M.2
  • 71
    • 0033586511 scopus 로고    scopus 로고
    • Boundary layer methods for Lipschitz domains in Riemannian manifolds
    • Mitrea M., Taylor M.: Boundary layer methods for Lipschitz domains in Riemannian manifolds. J. Funct. Anal. 163(2), 181-251 (1999).
    • (1999) J. Funct. Anal. , vol.163 , Issue.2 , pp. 181-251
    • Mitrea, M.1    Taylor, M.2
  • 72
    • 85121159562 scopus 로고    scopus 로고
    • p Hardy, and Hölder space results
    • p Hardy, and Hölder space results. Comm. Anal. Geom. 9(2), 369-421 (2001).
    • (2001) Comm. Anal. Geom. , vol.9 , Issue.2 , pp. 369-421
    • Mitrea, M.1    Taylor, M.2
  • 75
    • 0001623115 scopus 로고    scopus 로고
    • Regularity of the solutions of elliptic systems in polyhedral domains
    • Nicaise S.: Regularity of the solutions of elliptic systems in polyhedral domains. Bull. Belg. Math. Soc. Simon Stevin 4(3), 411-429 (1997).
    • (1997) Bull. Belg. Math. Soc. Simon Stevin , vol.4 , Issue.3 , pp. 411-429
    • Nicaise, S.1
  • 76
    • 0346251772 scopus 로고    scopus 로고
    • Transmission problems for the Laplace and elasticity operators: Regularity and boundary integral formulation
    • Nicaise S., Sändig A.-M.: Transmission problems for the Laplace and elasticity operators: Regularity and boundary integral formulation. Math. Models Methods Appl. Sci. 9(6), 855-898 (1999).
    • (1999) Math. Models Methods Appl. Sci. , vol.9 , Issue.6 , pp. 855-898
    • Nicaise, S.1    Sändig, A.-M.2
  • 77
    • 84980073094 scopus 로고
    • Estimates and existence of solutions of elliptic equations
    • Nirenberg L.: Estimates and existence of solutions of elliptic equations. Comm. Pure Appl. Math. 9, 509-529 (1956).
    • (1956) Comm. Pure Appl. Math. , vol.9 , pp. 509-529
    • Nirenberg, L.1
  • 78
    • 0000667107 scopus 로고
    • On Korn's second inequality
    • Nitsche J.A.: On Korn's second inequality. RAIRO Anal. Numér. 15(3), 237-248 (1981).
    • (1981) RAIRO Anal. Numér. , vol.15 , Issue.3 , pp. 237-248
    • Nitsche, J.A.1
  • 79
    • 0001817132 scopus 로고
    • The regularity of boundary value problems for the Lamé equations in a polygonal domain
    • Sändig A.-M., Richter U., Sändig R.: The regularity of boundary value problems for the Lamé equations in a polygonal domain. Rostock. Math. Kolloq. 36, 21-50 (1989).
    • (1989) Rostock. Math. Kolloq. , vol.36 , pp. 21-50
    • Sändig, A.-M.1    Richter, U.2    Sändig, R.3
  • 80
    • 0002592744 scopus 로고    scopus 로고
    • Regularity results for elliptic equations in Lipschitz domains
    • Savaré G.: Regularity results for elliptic equations in Lipschitz domains. J. Funct. Anal. 152(1), 176-201 (1998).
    • (1998) J. Funct. Anal. , vol.152 , Issue.1 , pp. 176-201
    • Savaré, G.1
  • 83
    • 0032105007 scopus 로고    scopus 로고
    • Mapping Properties of Pseudodifferential Operators on Manifolds with Bounded Geometry
    • Skrzypczak, L.: Mapping properties of pseudodifferential operators on manifolds with bounded geometry. J. Lond. Math. Soc. (2)57(3), 721-738 (1998).
    • (1998) J. Lond. Math. Soc. (2) , vol.57 , Issue.3 , pp. 721-738
    • Skrzypczak, L.1
  • 84
    • 85137367340 scopus 로고
    • The wedge under a concentrated couple: A paradox in the two-dimensional theory of elasticity
    • Sternberg E., Koiter W.: The wedge under a concentrated couple: A paradox in the two-dimensional theory of elasticity. J. Appl. Mech. 25, 575-581 (1958).
    • (1958) J. Appl. Mech. , vol.25 , pp. 575-581
    • Sternberg, E.1    Koiter, W.2
  • 85
    • 0009154957 scopus 로고
    • Princeton Mathematical Series, Princeton: Princeton University Press
    • Taylor M.: Pseudodifferential Operators, vol. 34, Princeton Mathematical Series, xi+452. Princeton University Press, Princeton (1981).
    • (1981) Pseudodifferential Operators , vol.34
    • Taylor, M.1
  • 88
    • 0009997534 scopus 로고    scopus 로고
    • Tools for PDE
    • American Mathematical Society, Providence, (Pseudodifferential operators, paradifferential operators, and layer potentials)
    • Taylor, M.: Tools for PDE, vol. 81, Mathematical Surveys and Monographs. American Mathematical Society, Providence, 2000 (Pseudodifferential operators, paradifferential operators, and layer potentials).
    • (2000) Mathematical Surveys and Monographs , vol.81
    • Taylor, M.1
  • 89
    • 84985320967 scopus 로고
    • Characterizations of function spaces on a complete Riemannian manifold with bounded geometry
    • Triebel H.: Characterizations of function spaces on a complete Riemannian manifold with bounded geometry. Math. Nachr. 130, 321-346 (1987).
    • (1987) Math. Nachr. , vol.130 , pp. 321-346
    • Triebel, H.1
  • 90
    • 48549113823 scopus 로고
    • Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
    • Verchota G.: Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains. J. Funct. Anal. 59(3), 572-611 (1984).
    • (1984) J. Funct. Anal. , vol.59 , Issue.3 , pp. 572-611
    • Verchota, G.1
  • 92
    • 84932296600 scopus 로고
    • Les opérateurs différentiels et pseudo-différentiels à une infinité de variables, les problèmes elliptiques et paraboliques
    • Astérisque, 2 et 3. Soc. Math. France, Paris
    • Vishik, M.I.: Les opérateurs différentiels et pseudo-différentiels à une infinité de variables, les problèmes elliptiques et paraboliques. In: Colloque International CNRS sur les équations aux Dérivées Partielles Linéaires (Univ. Paris-Sud, Orsay, 1972), pp. 342-362. Astérisque, 2 et 3. Soc. Math. France, Paris, 1973.
    • (1973) Colloque International CNRS sur les équations aux Dérivées Partielles Linéaires (Univ. Paris-Sud, Orsay, 1972) , pp. 342-362
    • Vishik, M.I.1
  • 93
    • 0002910639 scopus 로고
    • 1 projections into finite element spaces: Influence of a re-entrant corner
    • 1 projections into finite element spaces: Influence of a re-entrant corner. Math. Comp. 42(165), 1-8 (1984).
    • (1984) Math. Comp. , vol.42 , Issue.165 , pp. 1-8
    • Wahlbin, L.1
  • 94
    • 70350504045 scopus 로고
    • Local behavior in finite element methods
    • Handb. Numer. Anal., II. North-Holland, Amsterdam
    • Wahlbin, L.: Local behavior in finite element methods. In: Handbook of numerical analysis, vol. II, Handb. Numer. Anal., II, pp. 353-522. North-Holland, Amsterdam, 1991.
    • (1991) Handbook of Numerical Analysis , vol.II , pp. 353-522
    • Wahlbin, L.1
  • 96
    • 0001208702 scopus 로고
    • Tangents to an analytic variety
    • Whitney, H.: Tangents to an analytic variety. Ann. Math. (2)81, 496-549 (1965).
    • (1965) Ann. Math. (2) , vol.81 , pp. 496-549
    • Whitney, H.1
  • 97
    • 0003320023 scopus 로고
    • Weakly Differentiable Functions
    • Springer, New York, (Sobolev spaces and functions of bounded variation)
    • Ziemer, W.P.: Weakly Differentiable Functions, vol. 120, Graduate Texts in Mathematics. Springer, New York, 1989 (Sobolev spaces and functions of bounded variation).
    • (1989) Graduate Texts in Mathematics , vol.120
    • Ziemer, W.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.