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Volumn 216, Issue 1, 2004, Pages 141-171

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

Author keywords

Atomic estimates; Layer potentials; Lipschitz domains; Spectral radius; Transmission problems

Indexed keywords


EID: 4344709446     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jfa.2003.12.005     Document Type: Article
Times cited : (55)

References (34)
  • 1
    • 0010824377 scopus 로고
    • New spectral results for the electrostatic integral operator
    • Ahner J.F. Dyakin V.V. Raevskii V.Ya. New spectral results for the electrostatic integral operator J. Math. Anal. Appl. 185 1994 391-402
    • (1994) J. Math. Anal. Appl. , vol.185 , pp. 391-402
    • Ahner, J.F.1    Dyakin, V.V.2    Raevskii, V.Y.3
  • 3
    • 0002154729 scopus 로고
    • Linear operators in complete positive cones
    • Bonsall F.F. Linear operators in complete positive cones Proc. London Math. Soc. 8 1958 53-75
    • (1958) Proc. London Math. Soc. , vol.8 , pp. 53-75
    • Bonsall, F.F.1
  • 4
    • 84972578171 scopus 로고
    • The Neumann problem on Lipschitz domains in Hardy spaces of order less than one
    • Brown R.M. The Neumann problem on Lipschitz domains in Hardy spaces of order less than one Pacific J. Math. 171 1995 389-407
    • (1995) Pacific J. Math. , vol.171 , pp. 389-407
    • Brown, R.M.1
  • 6
    • 0000225785 scopus 로고
    • p-Neumann problem for Laplace's equation in a Lipschitz domain
    • p-Neumann problem for Laplace's equation in a Lipschitz domain Ann. of Math. 125 1987 437-465
    • (1987) Ann. of Math. , vol.125 , pp. 437-465
    • Dahlberg, B.1    Kenig, C.2
  • 7
    • 0000896312 scopus 로고
    • q-Estimates for the three-dimensional system of elastostatics on Lipschitz domains
    • C. Sadosky (Ed.), Dekker, NY
    • q-Estimates for the three-dimensional system of elastostatics on Lipschitz domains, in: C. Sadosky (Ed.), Lecture Notes in Pure and Applied Mathematics, Vol. 122, Dekker, NY, 1990, pp. 621-634
    • (1990) Lecture Notes in Pure and Applied Mathematics , vol.122 , pp. 621-634
    • Dahlberg, B.1    Kenig, C.2
  • 8
    • 0002412307 scopus 로고
    • Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari
    • De Giorgi E. Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. 3 1957 25-43
    • (1957) Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat. , vol.3 , pp. 25-43
    • De Giorgi, E.1
  • 9
    • 0041385035 scopus 로고
    • Open problems in singular integral theory
    • Derrick W. Open problems in singular integral theory J. Integral Equations Appl. 5 1993 23-28
    • (1993) J. Integral Equations Appl. , vol.5 , pp. 23-28
    • Derrick, W.1
  • 10
    • 0012948440 scopus 로고    scopus 로고
    • Semilinear Poisson problems in Sobolev - Besov spaces on Lipschitz domains
    • Dindoš M. Mitrea M. Semilinear Poisson problems in Sobolev - Besov spaces on Lipschitz domains Publ. Mat. 46 2002 353-403
    • (2002) Publ. Mat. , vol.46 , pp. 353-403
    • Dindoš, M.1    Mitrea, M.2
  • 11
    • 84880438084 scopus 로고
    • On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries
    • Escauriaza L. Fabes E. Verchota G. On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries Proc. Amer. Math. Soc. 115 1992 1069-1076
    • (1992) Proc. Amer. Math. Soc. , vol.115 , pp. 1069-1076
    • Escauriaza, L.1    Fabes, E.2    Verchota, G.3
  • 13
    • 0038229045 scopus 로고
    • The spectral radius of the classical layer potentials on convex domains, Partial differential equations with minimal smoothness and applications
    • Springer, New York, (Chicago, IL, 1990)
    • E. Fabes, M. Sand, J.-K. Seo, The spectral radius of the classical layer potentials on convex domains, Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), IMA Vol. Math. Appl., Vol. 42, Springer, New York, 1992, pp. 129-137
    • (1992) IMA Vol. Math. Appl. , vol.42 , pp. 129-137
    • Fabes, E.1    Sand, M.2    Seo, J.-K.3
  • 15
    • 0040335288 scopus 로고
    • Introduction to regularity theory for nonlinear elliptic systems
    • Birkhäuser Verlag, Basel
    • M. Giaquinta, Introduction to regularity theory for nonlinear elliptic systems, Lectures in Mathematics ETH Zürich, Birkhäuser Verlag, Basel, 1993
    • (1993) Lectures in Mathematics ETH Zürich
    • Giaquinta, M.1
  • 16
    • 84972551122 scopus 로고
    • A local version of real Hardy spaces
    • Goldberg D. A local version of real Hardy spaces Duke Math. J. 46 1979 27-42
    • (1979) Duke Math. J. , vol.46 , pp. 27-42
    • Goldberg, D.1
  • 17
    • 4344642452 scopus 로고
    • On the interpolation of sublinear operators
    • Janson S. On the interpolation of sublinear operators Studia Math. 75 1982 51-53
    • (1982) Studia Math. , vol.75 , pp. 51-53
    • Janson, S.1
  • 18
    • 22444454571 scopus 로고    scopus 로고
    • Stability of Fredholm properties on interpolation scales of quasi - Banach spaces and applications
    • Kalton N. Mitrea M. Stability of Fredholm properties on interpolation scales of quasi - Banach spaces and applications Trans. Amer. Math. Soc. 350 10 1998 3837-3901
    • (1998) Trans. Amer. Math. Soc. , vol.350 , Issue.10 , pp. 3837-3901
    • Kalton, N.1    Mitrea, M.2
  • 19
    • 0010499931 scopus 로고
    • p spaces on Lipschitz domains
    • p spaces on Lipschitz domains Amer. J. Math. 102 1980 129-163
    • (1980) Amer. J. Math. , vol.102 , pp. 129-163
    • Kenig, C.E.1
  • 20
    • 0000324134 scopus 로고
    • Elliptic boundary value problems in Lipschitz domains
    • Beijing Lectures in Harmonic Analysis , Beijing, 1984, pp. 131-183
    • C.E. Kenig, Elliptic boundary value problems in Lipschitz domains, Beijing Lectures in Harmonic Analysis , Beijing, 1984, pp. 131-183; Ann. of Math. Stud. 12 (1986)
    • (1984) Ann. of Math. Stud. , vol.12 , pp. 1986
    • Kenig, C.E.1
  • 21
    • 0003307061 scopus 로고
    • Harmonic analysis techniques for second order elliptic boundary value problems
    • Providence, RI: AMS
    • Kenig C.E. Harmonic analysis techniques for second order elliptic boundary value problems CBMS Regional Conference Series in Mathematics Vol. 83 1994 AMS Providence, RI
    • (1994) CBMS Regional Conference Series in Mathematics , vol.83
    • Kenig, C.E.1
  • 23
    • 0036002994 scopus 로고    scopus 로고
    • Layer potentials and Hodge decompositions in two dimensional Lipschitz domains
    • Mitrea D. Layer potentials and Hodge decompositions in two dimensional Lipschitz domains Math. Ann. 322 2002 75-101
    • (2002) Math. Ann. , vol.322 , pp. 75-101
    • Mitrea, D.1
  • 24
    • 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. Amer. Math. Soc. 150 713 2001
    • (2001) Mem. Amer. Math. Soc. , vol.150 , Issue.713
    • Mitrea, D.1    Mitrea, M.2    Taylor, M.3
  • 25
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential operators
    • Moser J. On Harnack's theorem for elliptic differential operators Comm. Pure Appl. Math. 14 1961 577-591
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 577-591
    • Moser, J.1
  • 26
    • 0001680091 scopus 로고
    • Continuity of the solutions of parabolic and elliptic equations
    • Nash J. Continuity of the solutions of parabolic and elliptic equations Amer. J. Math. 80 1957 931-954
    • (1957) Amer. J. Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 27
    • 0003890212 scopus 로고
    • Les méthodes directes en théorie des équations elliptiques
    • Academia, Éditeurs, Prague: Masson et Cie, Éditeurs, Paris
    • Nečas J. Les méthodes directes en théorie des équations elliptiques 1967 Masson et Cie, Éditeurs, Paris Academia, Éditeurs, Prague
    • (1967)
    • Nečas, J.1
  • 28
    • 0001653392 scopus 로고
    • On the Hölder continuity of solutions of second order elliptic equations in two variables
    • Piccinini L.C. Spagnolo S. On the Hölder continuity of solutions of second order elliptic equations in two variables Ann. Scuola Norm. Sup. Pisa 26 1972 391-402
    • (1972) Ann. Scuola Norm. Sup. Pisa , vol.26 , pp. 391-402
    • Piccinini, L.C.1    Spagnolo, S.2
  • 29
    • 0013326902 scopus 로고
    • p for the biharmonic equation on Lipschitz domains
    • p for the biharmonic equation on Lipschitz domains Amer. J. Math. 114 1992 923-972
    • (1992) Amer. J. Math. , vol.114 , pp. 923-972
    • Pipher, J.1    Verchota, G.2
  • 30
    • 0000494186 scopus 로고
    • Darstellung der Eigenwerte von Δ u+λ u=0 durch ein Randintegral
    • Rellich F. Darstellung der Eigenwerte von Δ u+λ u=0 durch ein Randintegral Math. Z. 46 1940 635-636
    • (1940) Math. Z. , vol.46 , pp. 635-636
    • Rellich, F.1
  • 32
    • 0042104210 scopus 로고
    • Isolated singularities of solutions of linear elliptic equations
    • Serrin J. Weinberger H.F. Isolated singularities of solutions of linear elliptic equations Amer. J. Math. 88 1966 258-272
    • (1966) Amer. J. Math. , vol.88 , pp. 258-272
    • Serrin, J.1    Weinberger, H.F.2
  • 33
    • 0141652970 scopus 로고    scopus 로고
    • Boundary value problems in Morrey spaces for elliptic systems in Lipschitz domains
    • Shen Z. Boundary value problems in Morrey spaces for elliptic systems in Lipschitz domains Amer. J. Math. 125 2003 1079-1115
    • (2003) Amer. J. Math. , vol.125 , pp. 1079-1115
    • Shen, Z.1
  • 34
    • 48549113823 scopus 로고
    • Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains
    • Verchota G. Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains J. Funct. Anal. 59 1984 572-611
    • (1984) J. Funct. Anal. , vol.59 , pp. 572-611
    • Verchota, G.1


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