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Volumn 54, Issue 1, 2005, Pages 99-142

Higher regularity in the layer potential theory for lipschitz domains

Author keywords

Fractional sobolev spaces; Higher regularity of solutions; Layer potentials; Lipschitz domains; Pointwise multipliers

Indexed keywords


EID: 17244362427     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2005.54.2668     Document Type: Article
Times cited : (32)

References (36)
  • 1
    • 0003237178 scopus 로고    scopus 로고
    • Grundlehren der Mathematischen Wissenschaften
    • [AH], Springer-Verlag, Berlin, ISBN 3-540-57060-8. MR1411441 (97j:46024)
    • [AH] DAVID R. ADAMS and LARS INGE HEDBERG, Function Spaces and Potential Theory, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 314, Springer-Verlag, Berlin, 1996, ISBN 3-540-57060-8. MR1411441 (97j:46024)
    • (1996) Fundamental Principles of Mathematical Sciences , vol.314
    • Adams, D.R.1    Hedberg, L.I.2
  • 2
    • 0001515481 scopus 로고
    • Singular integrals
    • [Ca1], (Proc. Sympos. Pure Math., Chicago, III., 1966), Algebras of Singular Integral Operators, R.I., MR0394309 (52 #15112)
    • [Ca1] ALBERTO P. CALDERÓN, Singular Integrals (Proc. Sympos. Pure Math., Chicago, III., 1966), Algebras of Singular Integral Operators, Amer. Math. Soc., Providence, R.I., 1967, pp. 18-55. MR0394309 (52 #15112)
    • (1967) Amer. Math. Soc., Providence , pp. 18-55
    • Calderón, A.P.1
  • 3
    • 77956921849 scopus 로고
    • Boundary value problems for the Laplace equation in Lipschitzian domains
    • [Ca2] , Recent Progress in Fourier Analysis (El Escorial, 1983), North-Holland, Amsterdam, MR848140 (87k:35062)
    • [Ca2] _, Boundary value problems for the Laplace equation in Lipschitzian domains, Recent Progress in Fourier Analysis (El Escorial, 1983), North-Holland Math. Stud., vol. 111, North-Holland, Amsterdam, 1985, pp. 33-48. MR848140 (87k:35062)
    • (1985) North-Holland Math. Stud. , vol.111 , pp. 33-48
  • 4
    • 0000410847 scopus 로고
    • 2 pour les courbes lipschitziennes
    • [CMM], MR672839 (84m:42027) (French)
    • 2 pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), 361-387. MR672839 (84m:42027) (French)
    • (1982) Ann. of Math. (2) , vol.116 , pp. 361-387
    • Coifman, R.R.1    Mcintosh, A.2    Meyer, Y.3
  • 5
    • 0000438610 scopus 로고
    • Boundary integral operators on Lipschitz domains: Elementary results
    • [Cos], MR937473 (89h:35090)
    • [Cos] MARTIN COSTABEL, Boundary integral operators on Lipschitz domains: elementary results, SIAM J. Math. Anal. 19 (1988), 613-626. MR937473 (89h:35090)
    • (1988) SIAM J. Math. Anal. , vol.19 , pp. 613-626
    • Costabel, M.1
  • 6
    • 84972551990 scopus 로고
    • Boundary value problems far the systems of elastostatics in Lipschitz domains
    • [DKV], MR975122 (90d:35259)
    • [DKV] BJÖRN E. J. DAHLBERG, CARLOS E. KENIG, and GREGORY C. VERCHOTA, Boundary value problems far the systems of elastostatics in Lipschitz domains, Duke Math. J. 57 (1988), 795-818. MR975122 (90d:35259)
    • (1988) Duke Math. J. , vol.57 , pp. 795-818
    • Dahlberg, B.E.J.1    Kenig, C.E.2    Verchota, G.C.3
  • 7
    • 84875092246 scopus 로고
    • Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains
    • [Fab], Miniconference on Linear Analysis and Function Spaces (Canberra, 1984), Austral. Nat. Univ., Canberra, MR825514 (87h:35292)
    • [Fab] EUGENE B. FABES, Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains, Miniconference on Linear Analysis and Function Spaces (Canberra, 1984), Proc. Centre Math. Anal. Austral. Nat. Univ., vol. 9, Austral. Nat. Univ., Canberra, 1985, pp. 27-45. MR825514 (87h:35292)
    • (1985) Proc. Centre Math. Anal. Austral. Nat. Univ. , vol.9 , pp. 27-45
    • Fabes, E.B.1
  • 9
    • 84865687708 scopus 로고
    • The dirichlet problem for the stokes system on lipschitz domains
    • [FKV], MR975121 (90d:35258)
    • [FKV] EUGENE B. FABES, CARLOS E. KENIG, and GREGORY C. VERCHOTA, The Dirichlet problem for the Stokes system on Lipschitz domains, Duke Math. J. 57 (1988), 769-793. MR975121 (90d:35258)
    • (1988) Duke Math. J. , vol.57 , pp. 769-793
    • Fabes, E.B.1    Kenig, C.E.2    Verchota, G.C.3
  • 10
    • 0348066037 scopus 로고
    • Problemi ai limiti lineari ellittici negli spazi di Sobolev con peso
    • [GG], MR0231046 (37 #6603) (Italian)
    • [GG] GIUSEPPE GEYMONAT and PIERRE GRISVARD, Problemi ai limiti lineari ellittici negli spazi di Sobolev con peso, Matematiche (Catania) 22 (1967), 212-249. MR0231046 (37 #6603) (Italian)
    • (1967) Matematiche (Catania) , vol.22 , pp. 212-249
    • Geymonat, G.1    Grisvard, P.2
  • 11
    • 0001623265 scopus 로고
    • The Dirichlet problem in nonsmooth domains
    • [JK1], MR607897 (84j:35076)
    • [JK1] DAVID S. JERISON and CARLOS E. KENIG, The Dirichlet problem in nonsmooth domains, Ann. of Math. (2) 113 (1981), 367-382. MR607897 (84j:35076)
    • (1981) Ann. of Math. (2) , vol.113 , pp. 367-382
    • Jerison, D.S.1    Kenig, C.E.2
  • 12
    • 84966201593 scopus 로고
    • The Neumann problem on Lipschitz domains
    • [JK2], MR598688(84a:35064)
    • [JK2] _, The Neumann problem on Lipschitz domains, Bull. Amer. Math. Soc. (N.S.) 4 (1981), 203-207. MR598688 (84a:35064)
    • (1981) Bull. Amer. Math. Soc. (N.S.) , vol.4 , pp. 203-207
  • 13
    • 84875107709 scopus 로고    scopus 로고
    • Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains
    • [Ke1], École Polytech., Palaiseau, 1984, p. Exp. No. 21, 13. MR811664 (87c:35142)
    • [Ke1] CARLOS E. KENIG, Boundary value problems of linear elastostatics and hydrostatics on Lipschitz domains, Goulaouic-Meyer-Schwartz Seminar, 1983-1984, École Polytech., Palaiseau, 1984, p. Exp. No. 21, 13. MR811664 (87c:35142)
    • Goulaouic-meyer-schwartz Seminar , pp. 1983-1984
    • Kenig, C.E.1
  • 14
    • 0003307061 scopus 로고    scopus 로고
    • Harmonic analysis techniques for second order elliptic boundary value problems
    • [Ke2], Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1994, ISBN 0-8218-0309-3. MR1282720 (96a:35040)
    • [Ke2] _, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS Regional Conference Series in Mathematics, vol. 83, Published for the Conference Board of the Mathematical Sciences, Washington, DC, 1994, ISBN 0-8218-0309-3. MR1282720 (96a:35040)
    • CBMS Regional Conference Series in Mathematics , vol.83
  • 15
    • 0000060009 scopus 로고
    • The trace inequality and eigenvalue estimates for Schrödinger operators
    • [KSa], MR867921 (88b:35150) (English, with French summary)
    • [KSa] RONALD KERMAN and ERIC SAWYER, The trace inequality and eigenvalue estimates for Schrödinger operators, Ann. Inst. Fourier (Grenoble) 36 (1986), 207-228. MR867921 (88b:35150) (English, with French summary)
    • (1986) Ann. Inst. Fourier (Grenoble) , vol.36 , pp. 207-228
    • Kerman, R.1    Sawyer, E.2
  • 16
    • 17244378007 scopus 로고
    • The Mathematical Theory of Viscous Incompressible Flow
    • [Lad], Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu. Gordon and Breach Science Publishers, New York, MR0254401 (40 #7610)
    • [Lad] OLGA A. LADYZHENSKAYA, The Mathematical Theory of Viscous Incompressible Flow, Second English edition, revised and enlarged. Translated from the Russian by Richard A. Silverman and John Chu. Mathematics and its Applications, Vol. 2, Gordon and Breach Science Publishers, New York, 1969. MR0254401 (40 #7610)
    • (1969) Mathematics and Its Applications , vol.2
    • Ladyzhenskaya, O.A.1
  • 17
    • 0039183235 scopus 로고
    • Asymptotics of the densities of harmonic potentials near the apex of a cone
    • [LeM], MR1050091 (91e:35075) (Russian)
    • [LeM] ALEXANDER V. LEVIN and VLADIMIR G. MAZ'YA, Asymptotics of the densities of harmonic potentials near the apex of a cone, Z. Anal. Anwendungen 8 (1989), 501-514. MR1050091 (91e:35075) (Russian)
    • (1989) Z. Anal. Anwendungen , vol.8 , pp. 501-514
    • Levin, A.V.1    Maz'ya, V.G.2
  • 18
    • 4944258348 scopus 로고    scopus 로고
    • Sharp estimates for Green potentials on nonsmooth domains
    • [MM], MR2092902
    • [MM] SVITLANA MAYBORODA and MARIUS MITREA, Sharp estimates for Green potentials on nonsmooth domains, Math. Res. Lett. 11 (2004), 481-492. MR2092902
    • (2004) Math. Res. Lett. , vol.11 , pp. 481-492
    • Mayboroda, S.1    Mitrea, M.2
  • 19
    • 0039183211 scopus 로고
    • The integral equations of potential theory in domains with piecewise smooth boundary
    • [Ma1]
    • [Ma1] VLADIMIR G. MAZ'YA, The integral equations of potential theory in domains with piecewise smooth boundary, Usp. Mat. Nauk 36 (1981), 229-230.
    • (1981) Usp. Mat. Nauk , vol.36 , pp. 229-230
    • Maz'ya, V.G.1
  • 20
    • 17244366374 scopus 로고
    • Boundary integral equations of elasticity in domains with piecewise smooth boundaries
    • [Ma2], Equadiff 6 (Brno, 1985), Springer, Berlin, MR877130 (88f:45006)
    • [Ma2] _, Boundary integral equations of elasticity in domains with piecewise smooth boundaries, Equadiff 6 (Brno, 1985), Lecture Notes in Math., vol. 1192, Springer, Berlin, 1986, pp. 235-242. MR877130 (88f:45006)
    • (1986) Lecture Notes in Math. , vol.1192 , pp. 235-242
  • 21
    • 84875107907 scopus 로고
    • On potential theory for the Lamé system in a domain with a piecewise smooth boundary
    • [Ma3] , (Russian) (Tbilisi, 1982), Tbilis. Gos. Univ., Tbilisi, 251.MR893883(88k:35062)(Russian)
    • [Ma3] _, On potential theory for the Lamé system in a domain with a piecewise smooth boundary, Partial differential equations and their applications (Russian) (Tbilisi, 1982), Tbilis. Gos. Univ., Tbilisi, 1986, pp. 123-129, 251. MR893883 (88k:35062) (Russian)
    • (1986) Partial Differential Equations and Their Applications , pp. 123-129
  • 22
    • 0003347537 scopus 로고
    • Boundary integral equations
    • [Ma4], Springer, Berlin, MR1098507 (93e:31003)
    • [Ma4] _, Boundary integral equations, Analysis, IV, Encyclopaedia Math. Sei., vol. 27, Springer, Berlin, 1991, pp. 127-222, MR1098507 (93e:31003)
    • (1991) Analysis, IV, Encyclopaedia Math. Sei. , vol.27 , pp. 127-222
  • 23
    • 0010347065 scopus 로고
    • Theory of multipliers in spaces of differentiable functions
    • [MS1], Pitman (Advanced Publishing Program), Boston, MA, ISBN 0-273-08638-3. MR785568 (87j:46074)
    • [MS1] VLADIMIR G. MAZ'YA and TATYANA O. SHAPOSHNIKOVA, Theory of Multipliers in Spaces of Differentiable Functions, Monographs and Studies in Mathematics, vol. 23, Pitman (Advanced Publishing Program), Boston, MA, 1985, ISBN 0-273-08638-3. MR785568 (87j:46074)
    • (1985) Monographs and Studies in Mathematics , vol.23
    • Maz'ya, V.G.1    Shaposhnikova, T.O.2
  • 24
    • 84875104906 scopus 로고    scopus 로고
    • Traces of multipliers in pairs of spaces of weighted Sobolev spaces
    • [MS2]
    • [MS2] _, Traces of multipliers in pairs of spaces of weighted Sobolev spaces, Journal of Function Spaces and Applications 3 (2005), 91-115.
    • (2005) Journal of Function Spaces and Applications , vol.3 , pp. 91-115
  • 25
    • 51249163850 scopus 로고
    • Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers
    • [MVe], MR1340271 (961:26021)
    • [MVe] VLADIMIR G. MAZ'YA and IGOR E. VERBITSKY, Capacitary inequalities for fractional integrals, with applications to partial differential equations and Sobolev multipliers, Ark. Mat. 33 (1995), 81-115. MR1340271 (961:26021)
    • (1995) Ark. Mat. , vol.33 , pp. 81-115
    • Maz'ya, V.G.1    Verbitsky, I.E.2
  • 26
    • 0033586511 scopus 로고    scopus 로고
    • Boundary layer methods for Lipschitz domains in Riemannian manifolds
    • [MT1], MR1680487 (2000b:35050)
    • [MT1] MARIUS MITREA and MICHAEL TAYLOR, Boundary layer methods for Lipschitz domains in Riemannian manifolds, J. Funct. Anal. 163 (1999), 181-251. MR1680487 (2000b:35050)
    • (1999) J. Funct. Anal. , vol.163 , pp. 181-251
    • Mitrea, M.1    Taylor, M.2
  • 27
    • 85121159562 scopus 로고    scopus 로고
    • P Hardy, and Hölder space results
    • [MT2], MR1846208 (2002B1012)
    • P Hardy, and Hölder space results, Comm. Anal. Geom. 9 (2001), 369-421. MR1846208 (2002B1012)
    • (2001) Comm. Anal. Geom. , vol.9 , pp. 369-421
  • 28
    • 0001929311 scopus 로고    scopus 로고
    • Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem
    • [MT3], MR1781631 (2002e:58044)
    • [MT3] _, Potential theory on Lipschitz domains in Riemannian manifolds: Sobolev-Besov space results and the Poisson problem, J. Funct. Anal. 176 (2000), 1-79. MR1781631 (2002e:58044)
    • (2000) J. Funct. Anal. , vol.176 , pp. 1-79
  • 29
    • 0034358481 scopus 로고    scopus 로고
    • Potential theory on Lipschitz domains in Riemannian manifolds: Hölder continuous metric tensors
    • [MT4], MR1765156 (2001h:35040)
    • [MT4]_, Potential theory on Lipschitz domains in Riemannian manifolds: Hölder continuous metric tensors, Comm. Partial Differential Equations 25 (2000), 1487-1536. MR1765156 (2001h:35040)
    • (2000) Comm. Partial Differential Equations , vol.25 , pp. 1487-1536
  • 30
    • 0037407945 scopus 로고    scopus 로고
    • Potential theory on Lipschitz domains in riemannian manifolds: The case of Dini metric tensors
    • [MT5], (electronic). MR1953534 (2003k:31004)
    • [MT5]_, Potential theory on Lipschitz domains in Riemannian manifolds: the case of Dini metric tensors, Trans. Amer. Math. Soc. 355 (2003), 1961-1985 (electronic). MR1953534 (2003k:31004)
    • (2003) Trans. Amer. Math. Soc. , vol.355 , pp. 1961-1985
  • 32
    • 0011290957 scopus 로고
    • Imbedding theorems for classes with weights
    • [Usp]
    • [Usp] STANISLAV V. USPENSKǏ, Imbedding theorems for classes with weights, Trudy Mat. Inst. Steklov. 60 (1961), 282-303, English translation: Amer Math. Soc. Transl. 87 (1970), 121-145. MR0136980 (25 #440) (Russian)
    • (1961) Trudy Mat. Inst. Steklov. , vol.60 , pp. 282-303
    • Uspenskǐ, S.V.1
  • 33
    • 17244377087 scopus 로고
    • [Usp], English translation: MR0136980 (25 #440) (Russian)
    • [Usp] STANISLAV V. USPENSKǏ, Imbedding theorems for classes with weights, Trudy Mat. Inst. Steklov. 60 (1961), 282-303, English translation: Amer Math. Soc. Transl. 87 (1970), 121-145. MR0136980 (25 #440) (Russian)
    • (1970) Amer Math. Soc. Transl. , vol.87 , pp. 121-145
  • 34
    • 0010299847 scopus 로고    scopus 로고
    • Nonlinear potentials and trace inequalities
    • [Ve], Rostock
    • [Ve] IGOR E. VERBITSKY, Nonlinear potentials and trace inequalities, The Maz'ya Anniversary Collection, Vol. 2 (Rostock, 1998), Oper. Theory Adv. Appl., vol. 110, Birkhäuser, Basel, 1999, pp. 323-343. MR1747901 (2001g:46086)
    • (1998) The Maz'ya Anniversary Collection , vol.2
    • Verbitsky, I.E.1
  • 35
    • 0010299847 scopus 로고    scopus 로고
    • [Ve] , Birkhäuser, Basel, MR1747901 (2001g:46086)
    • [Ve] IGOR E. VERBITSKY, Nonlinear potentials and trace inequalities, The Maz'ya Anniversary Collection, Vol. 2 (Rostock, 1998), Oper. Theory Adv. Appl., vol. 110, Birkhäuser, Basel, 1999, pp. 323-343. MR1747901 (2001g:46086)
    • (1999) Oper. Theory Adv. Appl. , vol.110 , pp. 323-343
  • 36
    • 48549113823 scopus 로고
    • Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains
    • [Ver], MR769382 (86e:35038)
    • [Ver] GREGORY C. VERCHOTA, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains, J. Funct. Anal. 59 (1984), 572-611. MR769382 (86e:35038)
    • (1984) J. Funct. Anal. , vol.59 , pp. 572-611
    • Verchota, G.C.1


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