메뉴 건너뛰기




Volumn 11, Issue 1, 2006, Pages 161-206

Sobolev spaces on lie manifolds and regularity for polyhedral domains

Author keywords

Analysis on complete manifolds; Lie manifolds; Polyhedral domains; Regularity

Indexed keywords


EID: 33845468329     PISSN: 14310635     EISSN: 14310635     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (55)

References (69)
  • 1
    • 0003796630 scopus 로고
    • Pure and Applied Mathematics, Academic Press, New York-London
    • R. A. Adams. Sobolev spaces. Pure and Applied Mathematics, Vol. 65. Academic Press, New York-London, 1975.
    • (1975) Sobolev Spaces , vol.65
    • Adams, R.A.1
  • 2
    • 0037900637 scopus 로고    scopus 로고
    • Yamabe metrics on cylindrical manifolds
    • K. Akutagawa and B. Botvinnik. Yamabe metrics on cylindrical manifolds. Geom. Funct. Anal., 13(2):259-333, 2003.
    • (2003) Geom. Funct. Anal. , vol.13 , Issue.2 , pp. 259-333
    • Akutagawa, K.1    Botvinnik, B.2
  • 3
    • 85161778280 scopus 로고    scopus 로고
    • Pseudodifferential operators on manifolds with a Lie structure at infinity
    • To appear in
    • B. Ammann, R. Lauter, and V. Nistor. Pseudodifferential operators on manifolds with a Lie structure at infinity. To appear in Annals of Math.
    • Annals of Math
    • Ammann, B.1    Lauter, R.2    Nistor, V.3
  • 4
    • 2942694417 scopus 로고    scopus 로고
    • On the geometry of Riemannian manifolds with a Lie structure at infinity
    • B. Ammann, R. Lauter, and V. Nistor. On the geometry of Riemannian manifolds with a Lie structure at infinity. Int. J. Math. Math. Sci., (1-4):161-193, 2004.
    • (2004) Int. J. Math. Math. Sci. , Issue.1-4 , pp. 161-193
    • Ammann, B.1    Lauter, R.2    Nistor, V.3
  • 5
    • 0030642438 scopus 로고    scopus 로고
    • Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: An approach in weighted Sobolev spaces
    • C. Amrouche, V. Girault, and J. Giroire. Dirichlet and Neumann exterior problems for the n-dimensional Laplace operator: an approach in weighted Sobolev spaces. J. Math. Pures Appl. (9), 76(1):55-81, 1997.
    • (1997) J. Math. Pures Appl. (9) , vol.76 , Issue.1 , pp. 55-81
    • Amrouche, C.1    Girault, V.2    Giroire, J.3
  • 6
    • 0002925943 scopus 로고    scopus 로고
    • Scalar curvature rigidity for asymptotically locally hyperbolic manifolds
    • L. Andersson and M. Dahl. Scalar curvature rigidity for asymptotically locally hyperbolic manifolds. Ann. Global Anal. Geom., 16(1):1-27, 1998.
    • (1998) Ann. Global Anal. Geom. , vol.16 , Issue.1 , pp. 1-27
    • Andersson, L.1    Dahl, M.2
  • 7
    • 0001676787 scopus 로고
    • Espaces de Sobolev sur les variétés riemanniennes
    • T. Aubin. Espaces de Sobolev sur les variétés riemanniennes. Bull. Sc. math., 100:149-173, 1970.
    • (1970) Bull. Sc. Math. , vol.100 , pp. 149-173
    • Aubin, T.1
  • 10
    • 17444419688 scopus 로고    scopus 로고
    • Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps
    • C. Bacuta, V. Nistor, and L. Zikatanov. Improving the rate of convergence of 'high order finite elements' on polygons and domains with cusps. Numerische Mathematik, 100:165-184, 2005.
    • (2005) Numerische Mathematik , vol.100 , pp. 165-184
    • Bacuta, C.1    Nistor, V.2    Zikatanov, L.3
  • 11
    • 29044437906 scopus 로고    scopus 로고
    • Improving the rate of convergence of high-order finite elements on polyhedra. I. A priori estimates
    • C. Bacuta, V. Nistor, and L. Zikatanov. 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.3
  • 12
    • 0004234640 scopus 로고
    • Springer-Verlag, Berlin. Grundlehren der Mathematischen Wissenschaften, No. 223
    • J. Bergh and J. Löfström. Interpolation spaces. An introduction. Springer-Verlag, Berlin, 1976. Grundlehren der Mathematischen Wissenschaften, No. 223.
    • (1976) Interpolation Spaces. An Introduction
    • Bergh, J.1    Löfström, J.2
  • 13
    • 84972535477 scopus 로고
    • Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
    • M. Cheeger, J. Gromov and M. Taylor. Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds. J. Differential Geom., 17(1):15-53, 1982.
    • (1982) J. Differential Geom. , vol.17 , Issue.1 , pp. 15-53
    • Cheeger, M.1    Gromov, J.2    Taylor, M.3
  • 14
    • 84972584101 scopus 로고
    • Spectrum of domains in Riemannian manifolds
    • H. Donnelly. Spectrum of domains in Riemannian manifolds. Illinois J. Math., 31(4):692-698, 1987.
    • (1987) Illinois J. Math. , vol.31 , Issue.4 , pp. 692-698
    • Donnelly, H.1
  • 15
    • 38249008655 scopus 로고
    • Normal solvability of elliptic boundary value problems on asymptotically flat manifolds
    • A. K. Erkip and E. Schrohe. Normal solvability of elliptic boundary value problems on asymptotically flat manifolds. J. Funct. Anal., 109:22-51, 1992.
    • (1992) J. Funct. Anal. , vol.109 , pp. 22-51
    • Erkip, A.K.1    Schrohe, E.2
  • 16
    • 85161783828 scopus 로고    scopus 로고
    • Partial differential equations. American Mathematical Society, Providence, RI
    • L. C. Evans. Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, 1998.
    • (1998) Graduate Studies in Mathematics , vol.19
    • Evans, L.C.1
  • 17
    • 0002253552 scopus 로고
    • The harmonic operator for exterior differential forms
    • M. P. Gaffney. The harmonic operator for exterior differential forms. Proc. Nat. Acad. Sci. U. S. A., 37:48-50, 1951.
    • (1951) Proc. Nat. Acad. Sci. U. S. A. , vol.37 , pp. 48-50
    • Gaffney, M.P.1
  • 18
    • 85161756072 scopus 로고    scopus 로고
    • Functional calculus of pseudodifferential boundary problems. Birkhäuser Boston Inc., Boston, MA, second edition
    • G. Grubb. Functional calculus of pseudodifferential boundary problems, volume 65 of Progress in Mathematics. Birkhäuser Boston Inc., Boston, MA, second edition, 1996.
    • (1996) Progress in Mathematics , vol.65
    • Grubb, G.1
  • 19
    • 0003920134 scopus 로고    scopus 로고
    • Sobolev spaces on Riemannian manifolds. Springer-Verlag, Berlin
    • E. Hebey. Sobolev spaces on Riemannian manifolds, volume 1635 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1996.
    • (1996) Lecture Notes in Mathematics , vol.1635
    • Hebey, E.1
  • 20
    • 85161771540 scopus 로고    scopus 로고
    • Nonlinear analysis on manifolds: Sobolev spaces and inequalities. New York University Courant Institute of Mathematical Sciences, New York
    • E. Hebey. Nonlinear analysis on manifolds: Sobolev spaces and inequalities, volume 5 of Courant Lecture Notes in Mathematics. New York University Courant Institute of Mathematical Sciences, New York, 1999.
    • (1999) Courant Lecture Notes in Mathematics , vol.5
    • Hebey, E.1
  • 21
    • 0001515477 scopus 로고
    • Pseudo-differential operators and hypoelliptic equations. Amer. Math. Soc., Providence, Rhode Island
    • L. Hörmander. Pseudo-differential operators and hypoelliptic equations, volume X of Proc. Symp. in Pure Math. - Singular Integrals, pages 138-183. Amer. Math. Soc., Providence, Rhode Island, 1967.
    • (1967) Proc. Symp. in Pure Math. - Singular Integrals , vol.10 , pp. 138-183
    • Hörmander, L.1
  • 22
    • 0041048056 scopus 로고
    • The analysis of linear partial differential operators, vol. 3. Pseudo-differential operators. Springer-Verlag, Berlin - Heidelberg - New York
    • L. Hörmander. The analysis of linear partial differential operators, vol. 3. Pseudo-differential operators, volume 274 of Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin - Heidelberg - New York, 1985.
    • (1985) Grundlehren der Mathematischen Wissenschaften , vol.274
    • Hörmander, L.1
  • 23
    • 0000271720 scopus 로고
    • The inhomogeneous Dirichlet problem in Lipschitz domains
    • D. Jerison and C. E. Kenig. 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.E.2
  • 24
    • 0001506343 scopus 로고
    • Homologie cyclique et K-theorie
    • M. Karoubi. Homologie cyclique et K-theorie. Asterisque, 149:1-147, 1987.
    • (1987) Asterisque , vol.149 , pp. 1-147
    • Karoubi, M.1
  • 25
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic equations in domains with conical or angular points
    • V. A. Kondrat'ev. 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
    • Kondrat'ev, V.A.1
  • 26
    • 0003619321 scopus 로고    scopus 로고
    • Elliptic boundary value problems in domains with point singularities. American Mathematical Society, Providence, RI
    • V. A. Kozlov, V. G. Maz'ya, and J. Rossmann. Elliptic boundary value problems in domains with point singularities, volume 52 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI, 1997.
    • (1997) Mathematical Surveys and Monographs , vol.52
    • Kozlov, V.A.1    Maz'ya, V.G.2    Rossmann, J.3
  • 27
    • 85088178261 scopus 로고    scopus 로고
    • Pseudodifferential analysis on conformally compact spaces
    • R. Lauter. Pseudodifferential analysis on conformally compact spaces. Mem. Amer. Math. Soc., 163(777), 2003.
    • (2003) Mem. Amer. Math. Soc. , vol.163 , Issue.777
    • Lauter, R.1
  • 28
    • 0000843689 scopus 로고    scopus 로고
    • Pseudodifferential analysis on continuous family groupoids
    • electronic
    • R. Lauter, B. Monthubert, and V. Nistor. Pseudodifferential analysis on continuous family groupoids. Doc. Math., 5:625-655 (electronic), 2000.
    • (2000) Doc. Math. , vol.5 , pp. 625-655
    • Lauter, R.1    Monthubert, B.2    Nistor, V.3
  • 30
    • 0043246651 scopus 로고    scopus 로고
    • Homology of pseudodifferential operators on manifolds with fibered cusps
    • electronic
    • R. Lauter and S. Moroianu. Homology of pseudodifferential operators on manifolds with fibered cusps. Trans. Amer. Math. Soc., 355(8):3009-3046 (electronic), 2003.
    • (2003) Trans. Amer. Math. Soc. , vol.355 , Issue.8 , pp. 3009-3046
    • Lauter, R.1    Moroianu, S.2
  • 31
    • 0001669291 scopus 로고    scopus 로고
    • Analysis of geometric operators on open manifolds: A groupoid approach
    • N. P. Landsman, M. Pflaum, and M. Schlichenmaier, editors, Quantization of Singular Symplectic Quotients. Birkhäuser, Basel - Boston - Berlin
    • R. Lauter and V. Nistor. Analysis of geometric operators on open manifolds: a groupoid approach. In N. P. Landsman, M. Pflaum, and M. Schlichenmaier, editors, Quantization of Singular Symplectic Quotients, volume 198 of Progress in Mathematics, pages 181-229. Birkhäuser, Basel - Boston - Berlin, 2001.
    • (2001) Progress in Mathematics , vol.198 , pp. 181-229
    • Lauter, R.1    Nistor, V.2
  • 35
    • 1642451027 scopus 로고    scopus 로고
    • Eigenvalue asymptotics for a class of mdelliptic ψdo's on manifolds with cylindrical exits
    • L. Maniccia and P. Panarese. Eigenvalue asymptotics for a class of mdelliptic ψdo's on manifolds with cylindrical exits. Ann. Mat. Pura Appl. (4), 181(3):283-308, 2002.
    • (2002) Ann. Mat. Pura Appl. (4) , vol.181 , Issue.3 , pp. 283-308
    • Maniccia, L.1    Panarese, P.2
  • 36
    • 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
  • 37
    • 84936145603 scopus 로고
    • Elliptic theory of differential edge operators. I
    • R. Mazzeo. Elliptic theory of differential edge operators. I. Commun. Partial Differ. Equations, 16(10):1615-1664, 1991.
    • (1991) Commun. Partial Differ. Equations , vol.16 , Issue.10 , pp. 1615-1664
    • Mazzeo, R.1
  • 38
    • 0002768927 scopus 로고
    • Pseudodifferential operators, corners and singular limits
    • Berlin - Heidelberg - New York. Springer-Verlag
    • R. B. Melrose. Pseudodifferential operators, corners and singular limits. In Proceeding of the International Congress of Mathematicians, Kyoto, pages 217-234, Berlin - Heidelberg - New York, 1990. Springer-Verlag.
    • (1990) Proceeding of the International Congress of Mathematicians, Kyoto , pp. 217-234
    • Melrose, R.B.1
  • 39
    • 0003744382 scopus 로고
    • Research Notes in Mathematics (Boston, Mass.). 4. Wellesley, MA: A. K. Peters, Ltd.
    • R. B. Melrose. The Atiyah-Patodi-Singer index theorem. Research Notes in Mathematics (Boston, Mass.). 4. Wellesley, MA: A. K. Peters, Ltd., 1993.
    • (1993) The Atiyah-Patodi-Singer Index Theorem
    • Melrose, R.B.1
  • 40
    • 0003468601 scopus 로고
    • Stanford Lectures. Cambridge University Press, Cambridge
    • R. B. Melrose. Geometric scattering theory. Stanford Lectures. Cambridge University Press, Cambridge, 1995.
    • (1995) Geometric Scattering Theory
    • Melrose, R.B.1
  • 41
    • 0033586511 scopus 로고    scopus 로고
    • Boundary layer methods for Lipschitz domains in Riemannian manifolds
    • M. Mitrea and M. Taylor. 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
  • 42
    • 22844454277 scopus 로고    scopus 로고
    • Pseudodifferential calculus on manifolds with corners and groupoids
    • B. Monthubert. Pseudodifferential calculus on manifolds with corners and groupoids. Proc. Amer. Math. Soc., 127(10):2871-2881, 1999.
    • (1999) Proc. Amer. Math. Soc. , vol.127 , Issue.10 , pp. 2871-2881
    • Monthubert, B.1
  • 43
    • 15244356371 scopus 로고
    • Lectures on pseudodifferential operators: regularity theorems and applications to nonelliptic problems. Princeton University Press, Princeton, N.J.
    • A. Nagel and E. Stein. Lectures on pseudodifferential operators: regularity theorems and applications to nonelliptic problems, volume 24 of Mathematical Notes. Princeton University Press, Princeton, N.J., 1979.
    • (1979) Mathematical Notes , vol.24
    • Nagel, A.1    Stein, E.2
  • 45
    • 0002814203 scopus 로고    scopus 로고
    • Pseudodifferential operators on groupoids
    • V. Nistor, A. Weinstein, and P. Xu. Pseudodifferential operators on groupoids. Pacific J. Math., 189:117-152, 1999.
    • (1999) Pacific J. Math. , vol.189 , pp. 117-152
    • Nistor, V.1    Weinstein, A.2    Xu, P.3
  • 46
    • 84979316769 scopus 로고
    • Über den Laplace-Operator auf Riemannschen Mannigfaltigkeiten mit diskontinuierlichen gruppen
    • W. Roelcke. Über den Laplace-Operator auf Riemannschen Mannigfaltigkeiten mit diskontinuierlichen Gruppen. Math. Nachr., 21:131-149, 1960.
    • (1960) Math. Nachr. , vol.21 , pp. 131-149
    • Roelcke, W.1
  • 47
    • 29044439078 scopus 로고
    • On two classes of weighted Sobolev-Slobodetskiǐ spaces in a dihedral angle
    • Partial differential equations, Part 1, 2 (Warsaw, 1990). Polish Acad. Sci., Warsaw
    • J. Rossmann. On two classes of weighted Sobolev-Slobodetskiǐ spaces in a dihedral angle. In Partial differential equations, Part 1, 2 (Warsaw, 1990), volume 2 of Banach Center Publ., 27, Part 1, pages 399-424. Polish Acad. Sci., Warsaw, 1992.
    • (1992) Banach Center Publ., 27, Part 1 , vol.2 , pp. 399-424
    • Rossmann, J.1
  • 48
    • 0039895548 scopus 로고    scopus 로고
    • Manifolds with boundary and of bounded geometry
    • T. Schick. Manifolds with boundary and of bounded geometry. Math. Nachr., 223:103-120, 2001.
    • (2001) Math. Nachr. , vol.223 , pp. 103-120
    • Schick, T.1
  • 49
    • 84972506352 scopus 로고
    • Conformal deformation of a Riemannian metric to constant scalar curvature
    • R. Schoen. Conformal deformation of a Riemannian metric to constant scalar curvature. J. Diff. Geom., 20:479-495, 1984.
    • (1984) J. Diff. Geom. , vol.20 , pp. 479-495
    • Schoen, R.1
  • 50
    • 34250263023 scopus 로고
    • On the proof of the positive mass conjecture in general relativity
    • R. Schoen and S.-T. Yau. On the proof of the positive mass conjecture in general relativity. Comm. Math. Phys., 65:45-76, 1979.
    • (1979) Comm. Math. Phys. , vol.65 , pp. 45-76
    • Schoen, R.1    Yau, S.-T.2
  • 51
    • 29244463784 scopus 로고
    • Proof of the positive mass theorem. II
    • R. Schoen and S.-T. Yau. Proof of the positive mass theorem. II. Comm. Math. Phys., 79:231-260, 1981.
    • (1981) Comm. Math. Phys. , vol.79 , pp. 231-260
    • Schoen, R.1    Yau, S.-T.2
  • 52
    • 0041095295 scopus 로고
    • Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces
    • E. Schrohe. Spectral invariance, ellipticity, and the Fredholm property for pseudodifferential operators on weighted Sobolev spaces. Ann. Global Anal. Geom., 10(3):237-254, 1992.
    • (1992) Ann. Global Anal. Geom. , vol.10 , Issue.3 , pp. 237-254
    • Schrohe, E.1
  • 53
    • 0001115649 scopus 로고    scopus 로고
    • Fréchet algebra techniques for boundary value problems: Fredholm criteria and functional calculus via spectral invariance
    • E. Schrohe. Fréchet algebra techniques for boundary value problems: Fredholm criteria and functional calculus via spectral invariance. Math. Nachr., 199:145-185, 1999.
    • (1999) Math. Nachr. , vol.199 , pp. 145-185
    • Schrohe, E.1
  • 54
    • 0001890943 scopus 로고
    • Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities II
    • Boundary value problems, Schrödinger operators, deformation quantization. Akademie Verlag, Berlin
    • E. Schrohe and B.-W. Schulze. Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities II. In Boundary value problems, Schrödinger operators, deformation quantization, volume 8 of Math. Top. Akademie Verlag, Berlin, 1995.
    • (1995) Math. Top , vol.8
    • Schrohe, E.1    Schulze, B.-W.2
  • 55
    • 0001823985 scopus 로고
    • Spectral theory of elliptic operators on noncompact manifolds
    • M. A. Shubin. Spectral theory of elliptic operators on noncompact manifolds. Astérisque, 207:5, 35-108, 1992.
    • (1992) Astérisque , vol.207 , Issue.5 , pp. 35-108
    • Shubin, M.A.1
  • 57
    • 0032105007 scopus 로고    scopus 로고
    • Mapping properties of pseudodifferential operators on manifolds with bounded geometry
    • L. Skrzypczak. Mapping properties of pseudodifferential operators on manifolds with bounded geometry. J. London Math. Soc. (2), 57(3):721-738, 1998.
    • (1998) J. London Math. Soc. (2) , vol.5 , Issue.73 , pp. 721-738
    • Skrzypczak, L.1
  • 59
    • 0009154957 scopus 로고
    • Pseudodifferential operators. Princeton University Press, Princeton, N.J.
    • M. Taylor. Pseudodifferential operators, volume 34 of Princeton Mathematical Series. Princeton University Press, Princeton, N.J., 1981.
    • (1981) Princeton Mathematical Series , vol.34
    • Taylor, M.1
  • 60
    • 33646752516 scopus 로고    scopus 로고
    • Partial differential equations I, Basic theory. Springer-Verlag, New York
    • M. Taylor. Partial differential equations I, Basic theory, volume 115 of Applied Mathematical Sciences. Springer-Verlag, New York, 1995.
    • (1995) Applied Mathematical Sciences , vol.115
    • Taylor, M.1
  • 61
    • 33646752516 scopus 로고    scopus 로고
    • Partial differential equations II, Qualitative studies of linear equations. Springer-Verlag, New York
    • M. Taylor. Partial differential equations II, Qualitative studies of linear equations, volume 116 of Applied Mathematical Sciences. Springer-Verlag, New York, 1996.
    • (1996) Applied Mathematical Sciences , vol.116
    • Taylor, M.1
  • 62
    • 33646752516 scopus 로고    scopus 로고
    • Partial differential equations III, Nonlinear equations. Springer-Verlag, New York
    • M. Taylor. Partial differential equations III, Nonlinear equations, volume 117 of Applied Mathematical Sciences. Springer-Verlag, New York, 1997.
    • (1997) Applied Mathematical Sciences , vol.117
    • Taylor, M.1
  • 63
    • 0000384573 scopus 로고
    • Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds
    • H. Triebel. Spaces of Besov-Hardy-Sobolev type on complete Riemannian manifolds. Ark. Mat., 24(2):299-337, 1986.
    • (1986) Ark. Mat. , vol.24 , Issue.2 , pp. 299-337
    • Triebel, H.1
  • 64
    • 84985320967 scopus 로고
    • Characterizations of function spaces on a complete Riemannian manifold with bounded geometry
    • H. Triebel. 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
  • 65
    • 0002708910 scopus 로고    scopus 로고
    • Propagation of singularities in many-body scattering
    • A. Vasy. Propagation of singularities in many-body scattering. Ann. Sci. École Norm. Sup. (4), 34(3):313-402, 2001.
    • (2001) Ann. Sci. École Norm. Sup. (4) , vol.34 , Issue.3 , pp. 313-402
    • Vasy, A.1
  • 66
    • 0034349282 scopus 로고    scopus 로고
    • Semiclassical estimates in asymptotically Euclidean scattering
    • A. Vasy and M. Zworski. Semiclassical estimates in asymptotically Euclidean scattering. Comm. Math. Phys., 212(1):205-217, 2000.
    • (2000) Comm. Math. Phys. , vol.212 , Issue.1 , pp. 205-217
    • Vasy, A.1    Zworski, M.2
  • 67
    • 48549113823 scopus 로고
    • Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
    • G. C. Verchota. 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.C.1
  • 68
    • 84867963270 scopus 로고    scopus 로고
    • A multidirectional Dirichlet problem
    • G. C. Verchota and A. L. Vogel. A multidirectional Dirichlet problem. J. Geom. Anal., 13(3):495-520, 2003.
    • (2003) J. Geom. Anal. , vol.13 , Issue.3 , pp. 495-520
    • Verchota, G.C.1    Vogel, A.L.2
  • 69
    • 33744727108 scopus 로고
    • A new proof of the positive energy theorem
    • E. Witten. A new proof of the positive energy theorem. Comm. Math. Phys., 80:381-402, 1981.
    • (1981) Comm. Math. Phys. , vol.80 , pp. 381-402
    • Witten, E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.