메뉴 건너뛰기




Volumn 3, Issue 2, 1997, Pages 131-192

Vector Potential Theory on Nonsmooth Domains in R3 and Applications to Electromagnetic Scattering

Author keywords

Lipschitz domains; Maxwell equations; Scattering; Vector layer potentials

Indexed keywords


EID: 1842781204     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02649132     Document Type: Article
Times cited : (104)

References (98)
  • 2
    • 0001558075 scopus 로고
    • The method of layer potentials for the heat equation in Lipschitz cylinders
    • Brown, R. (1989). The method of layer potentials for the heat equation in Lipschitz cylinders. Amer. J. Math. 111, 339-379.
    • (1989) Amer. J. Math. , vol.111 , pp. 339-379
    • Brown, R.1
  • 3
    • 84966229383 scopus 로고
    • The initial-Neumann problem for the heat equation in Lipschitz cylinders
    • Brown, R. (1990). The initial-Neumann problem for the heat equation in Lipschitz cylinders. Trans. Amer. Math. Soc. 320, 1-52.
    • (1990) Trans. Amer. Math. Soc. , vol.320 , pp. 1-52
    • Brown, R.1
  • 5
    • 0001059379 scopus 로고
    • The initial-Dirichlet problem for a fourth-order parabolic equation in Lipschitz cylinders
    • Brown, R. and Shen, Z. (1990). The initial-Dirichlet problem for a fourth-order parabolic equation in Lipschitz cylinders. Indiana Univ. Math. J. 39, 1313-1353.
    • (1990) Indiana Univ. Math. J. , vol.39 , pp. 1313-1353
    • Brown, R.1    Shen, Z.2
  • 6
    • 0242505464 scopus 로고
    • The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary
    • Birman, M. Sh. and Solomyak, M. Z. (1987). The Weyl asymptotics of the spectrum of the Maxwell operator for domains with a Lipschitz boundary. Vestnik Leningrads. Univ. Mat. Mekh. Astronom. 20, 23-28.
    • (1987) Vestnik Leningrads. Univ. Mat. Mekh. Astronom. , vol.20 , pp. 23-28
    • Birman, M.Sh.1    Solomyak, M.Z.2
  • 8
    • 0009154468 scopus 로고
    • The multipole expansion of radiation fields
    • Calderón, A. (1954). The multipole expansion of radiation fields. J. Rational Mech. Anal. 3, 523-537.
    • (1954) J. Rational Mech. Anal. , vol.3 , pp. 523-537
    • Calderón, A.1
  • 9
    • 0001934924 scopus 로고
    • Boundary value problems in Lipschitz domains
    • Elsevier, Amsterdam
    • Calderón, A. (1985). Boundary value problems in Lipschitz domains. Recent Progress in Fourier Analysis. Elsevier, Amsterdam, 33-48.
    • (1985) Recent Progress in Fourier Analysis , pp. 33-48
    • Calderón, A.1
  • 10
    • 0007213471 scopus 로고
    • Commutators, singular integrals on Lipschitz curves and applications
    • Calderón, A. (1980). Commutators, singular integrals on Lipschitz curves and applications. Proc. Int. Congress Math., Helsinki 1978 1, 85-96.
    • (1980) Proc. Int. Congress Math., Helsinki , vol.1978 , Issue.1 , pp. 85-96
    • Calderón, A.1
  • 13
    • 84966261604 scopus 로고
    • Extensions of Hardy spaces and their use in analysis
    • Coifman, R. and Weiss, G. (1977). Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc. (N.S.) 83, 569-645.
    • (1977) Bull. Amer. Math. Soc. (N.S.) , vol.83 , pp. 569-645
    • Coifman, R.1    Weiss, G.2
  • 16
    • 84988168833 scopus 로고
    • A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains
    • Costabel, M. (1990). A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains. Math. Meth. Appl. Sci. 12, 365-368.
    • (1990) Math. Meth. Appl. Sci. , vol.12 , pp. 365-368
    • Costabel, M.1
  • 17
    • 0017727486 scopus 로고
    • On estimates of harmonic measure
    • Dahlberg, B. E. J. (1977). On estimates of harmonic measure. Arch. Rational Mech. Anal. 65, 272-288.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , pp. 272-288
    • Dahlberg, B.E.J.1
  • 19
    • 0000941796 scopus 로고
    • q-Estimates for Green potentials in Lipschitz domains
    • q-Estimates for Green potentials in Lipschitz domains. Math. Scand. 44, 149-170.
    • (1979) Math. Scand. , vol.44 , pp. 149-170
    • Dahlberg, B.E.J.1
  • 20
    • 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, 437-465.
    • (1987) Ann. of Math. , vol.125 , pp. 437-465
    • Dahlberg, B.1    Kenig, C.2
  • 21
    • 85056072902 scopus 로고
    • p estimates for the three-dimension system of elastostatics on Lipschitz domains
    • C. Sadosky ed.
    • p estimates for the three-dimension system of elastostatics on Lipschitz domains. Lecture Notes in Pure and Appl. Math. (C. Sadosky ed.) 122, 621-634.
    • (1989) Lecture Notes in Pure and Appl. Math. , vol.122 , pp. 621-634
    • Dahlberg, B.1    Kenig, C.2
  • 22
    • 0010705591 scopus 로고
    • The Dirichlet problem for the biharmonic equation in a Lipschitz domain
    • Dahlberg, B., Kenig, C., and Verchota, G. (1986). The Dirichlet problem for the biharmonic equation in a Lipschitz domain. Ann. Inst. Fourier (Grenoble) 36, 109-135.
    • (1986) Ann. Inst. Fourier (Grenoble) , vol.36 , pp. 109-135
    • Dahlberg, B.1    Kenig, C.2    Verchota, G.3
  • 23
    • 84972551990 scopus 로고
    • Boundary value problems for the systems of elastostatics in Lipschitz domains
    • Dahlberg, B., Kenig, C., and Verchota, G. (1988). Boundary value problems for the systems of elastostatics in Lipschitz domains. Duke Math. J. 57, 795-818.
    • (1988) Duke Math. J. , vol.57 , pp. 795-818
    • Dahlberg, B.1    Kenig, C.2    Verchota, G.3
  • 25
    • 0001396210 scopus 로고
    • The double layer potential operator over polyhedral domains I: Solvability in weighted Sobolev spaces
    • Elschner, J. (1992). The double layer potential operator over polyhedral domains I: Solvability in weighted Sobolev spaces. Appl. Anal. 45, 117-134.
    • (1992) Appl. Anal. , vol.45 , pp. 117-134
    • Elschner, J.1
  • 26
    • 0001926062 scopus 로고
    • Layer potential methods for boundary value problems on Lipschitz domains
    • Potential Theory, Surveys and Problems (J. Král et al., eds.). Springer-Verlag, New York
    • Fabes, E. B. (1988). Layer potential methods for boundary value problems on Lipschitz domains. Potential Theory, Surveys and Problems (J. Král et al., eds.). Lecture Notes in Math. 1344. Springer-Verlag, New York, 55-80.
    • (1988) Lecture Notes in Math. , vol.1344 , pp. 55-80
    • Fabes, E.B.1
  • 29
    • 84865687708 scopus 로고
    • The Dirichlet problem for the Stokes system on Lipschitz domains
    • Fabes, E., Kenig, C., and Verchota, G. (1988). The Dirichlet problem for the Stokes system on Lipschitz domains. Duke Math. J. 5, 769-793.
    • (1988) Duke Math. J. , vol.5 , pp. 769-793
    • Fabes, E.1    Kenig, C.2    Verchota, G.3
  • 31
    • 0002780973 scopus 로고
    • The theory of weights and the Dirichlet problem for elliptic equations
    • Fefferman, R. A., Kenig, C. E., and Pipher, J. (1991). The theory of weights and the Dirichlet problem for elliptic equations. Ann. Math. (2) 134, 65-124.
    • (1991) Ann. Math. , vol.134 , Issue.2 , pp. 65-124
    • Fefferman, R.A.1    Kenig, C.E.2    Pipher, J.3
  • 34
    • 0004088932 scopus 로고
    • Pitman Advanced Publishing Program, Boston, London, and Melbourne
    • Grisvard, P. (1985). Elliptic Problems in Nonsmooth Domains. Pitman Advanced Publishing Program, Boston, London, and Melbourne.
    • (1985) Elliptic Problems in Nonsmooth Domains
    • Grisvard, P.1
  • 35
    • 0001534201 scopus 로고
    • On uniqueness in the inverse transmission scattering problem
    • Isakov, V. (1990). On uniqueness in the inverse transmission scattering problem, Comm. Partial Differential Equations 15, 1565-1587.
    • (1990) Comm. Partial Differential Equations , vol.15 , pp. 1565-1587
    • Isakov, V.1
  • 36
    • 0040817437 scopus 로고
    • Uniqueness and stability in multi-dimensional inverse problems
    • Isakov, V. (1993). Uniqueness and stability in multi-dimensional inverse problems. Inverse Problems 9, 579-621.
    • (1993) Inverse Problems , vol.9 , pp. 579-621
    • Isakov, V.1
  • 37
    • 21344465813 scopus 로고    scopus 로고
    • Boundary estimates for harmonic forms
    • Iwaniec, T., Mitrea, M., and Scott, C. (1996). Boundary estimates for harmonic forms. Proc. Amer. Math. Soc. 124, No. 5, 1467-1471.
    • (1996) Proc. Amer. Math. Soc. , vol.124 , Issue.5 , pp. 1467-1471
    • Iwaniec, T.1    Mitrea, M.2    Scott, C.3
  • 38
    • 1842639733 scopus 로고
    • On the spectra of the higher dimensional Maxwell operators
    • Harmonic Analysis and Operator Theory G. Mendoza et al., eds., Providence, RI
    • Jawerth, B. and Mitrea, M. (1995). On the spectra of the higher dimensional Maxwell operators. Harmonic Analysis and Operator Theory (G. Mendoza et al., eds.). Contemp. Math. Amer. Math. Soc., Providence, RI., 309-315.
    • (1995) Contemp. Math. Amer. Math. Soc. , pp. 309-315
    • Jawerth, B.1    Mitrea, M.2
  • 40
    • 84966201593 scopus 로고
    • The Neumann problem on Lipschitz domains
    • Jerison, D. and Kenig, C. (1981). The Neumann problem on Lipschitz domains. Bull. Amer. Math. Soc. 4, 203-207.
    • (1981) Bull. Amer. Math. Soc. , vol.4 , pp. 203-207
    • Jerison, D.1    Kenig, C.2
  • 41
    • 1842740583 scopus 로고
    • The functional calculus for the Laplacian on Lipschitz domains
    • Jerison, D. and Kenig, C. (1989). The functional calculus for the Laplacian on Lipschitz domains. J. Eq. Deriv. Part., IV.1-IV. 10.
    • (1989) J. Eq. Deriv. Part.
    • Jerison, D.1    Kenig, C.2
  • 42
    • 0000271720 scopus 로고
    • The inhomogeneous Dirichlet problem in Lipschitz domains
    • Jerison, D. and Kenig, C. (1995). The inhomogeneous Dirichlet problem in Lipschitz domains. J. Funct. Anal. 130, No. 1, 161-219.
    • (1995) J. Funct. Anal. , vol.130 , Issue.1 , pp. 161-219
    • Jerison, D.1    Kenig, C.2
  • 43
    • 0042046095 scopus 로고
    • The eigenvalues of a cavity resonator
    • Jones, D. S. (1988). The eigenvalues of a cavity resonator, Quart. J. Mech. Appl. Math. 41, 469-477.
    • (1988) Quart. J. Mech. Appl. Math. , vol.41 , pp. 469-477
    • Jones, D.S.1
  • 47
    • 0001403911 scopus 로고
    • The Neumann problem for elliptic equations with non-smooth coefficients
    • Kenig, C. and Pipher, J. (1993). The Neumann problem for elliptic equations with non-smooth coefficients. Inventiones Math. 113, 447-509.
    • (1993) Inventiones Math. , vol.113 , pp. 447-509
    • Kenig, C.1    Pipher, J.2
  • 49
    • 0000532530 scopus 로고
    • Uniqueness in inverse obstacle scattering
    • Kirsch, A. and Kress, R. (1993). Uniqueness in inverse obstacle scattering. Inverse Problems 9, 285-299.
    • (1993) Inverse Problems , vol.9 , pp. 285-299
    • Kirsch, A.1    Kress, R.2
  • 50
    • 0000309125 scopus 로고
    • Boundary value problems for elliptic equations in regions with conical or angular points
    • Kondrat'ev, V. A. (1967). Boundary value problems for elliptic equations in regions with conical or angular points. Trans. Moscow Math. Soc. 16, 227-313.
    • (1967) Trans. Moscow Math. Soc. , vol.16 , pp. 227-313
    • Kondrat'ev, V.A.1
  • 61
    • 1842639745 scopus 로고
    • Thesis. University of Minnesota
    • Mitrea, D. (1995). Thesis. University of Minnesota.
    • (1995)
    • Mitrea, D.1
  • 63
    • 0000292466 scopus 로고
    • Electromagnetic scattering on nonsmooth domains
    • Mitrea, M. (1994). Electromagnetic scattering on nonsmooth domains. Math. Res. Lett. 1, 639-646.
    • (1994) Math. Res. Lett. , vol.1 , pp. 639-646
    • Mitrea, M.1
  • 64
    • 84973999445 scopus 로고
    • The method of layer potentials in electro-magnetic scattering theory on non-smooth domains
    • Mitrea, M. (1995). The method of layer potentials in electro-magnetic scattering theory on non-smooth domains. Duke Math. J. 77, 111-133.
    • (1995) Duke Math. J. , vol.77 , pp. 111-133
    • Mitrea, M.1
  • 65
    • 0040628401 scopus 로고
    • Initial boundary value problems for the parabolic Maxwell system in Lipschitz cylinders
    • Mitrea, M. (1995). Initial boundary value problems for the parabolic Maxwell system in Lipschitz cylinders. Indiana Math. J. 44, No. 3, 797-813.
    • (1995) Indiana Math. J. , vol.44 , Issue.3 , pp. 797-813
    • Mitrea, M.1
  • 66
    • 0002326605 scopus 로고
    • 1 and Lipschitz domains
    • Proc. Conf. on Clifford Algebras in Analysis (J. Ryan, ed.). C.R.C. Press Inc., Boca Raton, FL
    • 1 and Lipschitz domains. Proc. Conf. on Clifford Algebras in Analysis (J. Ryan, ed.). Studies in Advanced Mathematics. C.R.C. Press Inc., Boca Raton, FL, 297-308.
    • (1955) Studies in Advanced Mathematics , pp. 297-308
    • Mitrea, M.1    Torres, R.2    Welland, G.3
  • 67
    • 0009304641 scopus 로고
    • Über die Beugung elektromagnetischer Schwingungen an endlichen homogenen Körpern
    • Müller, C. (1951). Über die Beugung elektromagnetischer Schwingungen an endlichen homogenen Körpern. Math. Ann. 123, 345-378.
    • (1951) Math. Ann. , vol.123 , pp. 345-378
    • Müller, C.1
  • 69
    • 0002084784 scopus 로고
    • Greensche Tensoren und asymptotische Gesetze der elektromagnetischen Hohlraumschwingungen
    • Müller, C. and Niemeyer, H. (1961). Greensche Tensoren und asymptotische Gesetze der elektromagnetischen Hohlraumschwingungen. Arch. Rational Mech. Anal. 7, 305-348.
    • (1961) Arch. Rational Mech. Anal. , vol.7 , pp. 305-348
    • Müller, C.1    Niemeyer, H.2
  • 71
    • 85176129448 scopus 로고
    • New bounds in harmonic and biharmonic problems
    • Payne, L. and Weinberger, H. (1954). New bounds in harmonic and biharmonic problems. J. Math. Phys. 33, 291-307.
    • (1954) J. Math. Phys. , vol.33 , pp. 291-307
    • Payne, L.1    Weinberger, H.2
  • 72
    • 0001387055 scopus 로고
    • An elementary proof for a compact embedding result in generalized electromagnetic theory
    • Picard, R. (1984). An elementary proof for a compact embedding result in generalized electromagnetic theory. Math. Z. 187, 151-164.
    • (1984) Math. Z. , vol.187 , pp. 151-164
    • Picard, R.1
  • 73
    • 0013326902 scopus 로고
    • p for biharmonic functions on Lipschitz domains
    • p for biharmonic functions on Lipschitz domains. Amer. J. Math. 114, 923-972.
    • (1992) Amer. J. Math. , vol.114 , pp. 923-972
    • Pipher, J.1    Verchota, G.2
  • 74
    • 0002693554 scopus 로고
    • Dilation invariant estimates and the boundary Garding inequality
    • to appear
    • Pipher, J. and Verchota, G. (1995). Dilation invariant estimates and the boundary Garding inequality. Ann. of Math, (to appear).
    • (1995) Ann. of Math
    • Pipher, J.1    Verchota, G.2
  • 75
    • 0001129736 scopus 로고    scopus 로고
    • Über die Randwertaufgaben beim logarithmischen potential
    • Radon, J. Über die Randwertaufgaben beim logarithmischen potential. Sitzungsber. Akad. Wiss. 128, 1123-1167.
    • Sitzungsber. Akad. Wiss. , vol.128 , pp. 1123-1167
    • Radon, J.1
  • 78
    • 0000494186 scopus 로고
    • Darstellung der cigenwerte von Δu + λu durch ein Radintegral
    • Rellich, F. (1940). Darstellung der cigenwerte von Δu + λu durch ein Radintegral. Math. Z. 46, 635-646.
    • (1940) Math. Z. , vol.46 , pp. 635-646
    • Rellich, F.1
  • 79
    • 1842740586 scopus 로고
    • On the asymptotic behavior of the spectrum of the Maxwell operator
    • Safarov, Yu. G. (1984). On the asymptotic behavior of the spectrum of the Maxwell operator. J. Soviet Math. 27, 2655-2661.
    • (1984) J. Soviet Math. , vol.27 , pp. 2655-2661
    • Safarov, Yu.G.1
  • 80
    • 0004593401 scopus 로고
    • On an inequality of Friedrichs
    • Saranen, J. (1982). On an inequality of Friedrichs. Math. Scand. 51, 310-322.
    • (1982) Math. Scand. , vol.51 , pp. 310-322
    • Saranen, J.1
  • 81
    • 0009155598 scopus 로고
    • On solutions of Maxwell's equations in an exterior region
    • Saunders, W. K. (1952). On solutions of Maxwell's equations in an exterior region. Proc. Nat. Acad. Sci. U.S.A. 38, 342-348.
    • (1952) Proc. Nat. Acad. Sci. U.S.A. , vol.38 , pp. 342-348
    • Saunders, W.K.1
  • 82
    • 0001318987 scopus 로고
    • Boundary value problems for parabolic Lamé systems and a nonstationary linearized system of Navier-Stokes equations in Lipschitz cylinders
    • Shen, Z. (1991). Boundary value problems for parabolic Lamé systems and a nonstationary linearized system of Navier-Stokes equations in Lipschitz cylinders. Amer. J. Math. 113, 293-373.
    • (1991) Amer. J. Math. , vol.113 , pp. 293-373
    • Shen, Z.1
  • 83
    • 0001555468 scopus 로고
    • A note on the Dirichlet problem for the Stokes system in Lipschitz domains
    • Shen, Z. (1995). A note on the Dirichlet problem for the Stokes system in Lipschitz domains. Proc. Amer. Math. Soc. 123, 801-811.
    • (1995) Proc. Amer. Math. Soc. , vol.123 , pp. 801-811
    • Shen, Z.1
  • 89
    • 0000805133 scopus 로고
    • Inverse boundary value problems and applications
    • Soc. Math. France, Montrouge
    • Uhlmann, G. (1992). Inverse boundary value problems and applications. Astérisque 207. Soc. Math. France, Montrouge.
    • (1992) Astérisque , vol.207
    • Uhlmann, G.1
  • 90
    • 0039417556 scopus 로고
    • Inverse boundary value problems for first order perturbations of the Laplacian
    • Amer. Math. Soc., Providence, RI
    • Uhlmann, G. (1994). Inverse boundary value problems for first order perturbations of the Laplacian. Lectures in Appl. Math. 30. Amer. Math. Soc., Providence, RI, 245-258.
    • (1994) Lectures in Appl. Math. , vol.30 , pp. 245-258
    • Uhlmann, G.1
  • 91
    • 84972510211 scopus 로고
    • A remark on functions of bounded mean oscillations and bounded harmonic functions
    • [91 ] Varopoulos, N. (1977). A remark on functions of bounded mean oscillations and bounded harmonic functions. Pacific J. Math. 74, 257-259.
    • (1977) Pacific J. Math. , vol.74 , pp. 257-259
    • Varopoulos, N.1
  • 93
    • 48549113823 scopus 로고
    • Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains
    • Verchota, G. (1984). Layer potentials and boundary value problems for Laplace's equation in Lipschitz domains. J. Funct. Anal. 59, 572-611.
    • (1984) J. Funct. Anal. , vol.59 , pp. 572-611
    • Verchota, G.1
  • 94
    • 84979103896 scopus 로고
    • A local compactness theorem for Maxwell's equations
    • Weber, C. (1980). A local compactness theorem for Maxwell's equations. Math. Meth. Appl. Sci. 2, 12-25.
    • (1980) Math. Meth. Appl. Sci. , vol.2 , pp. 12-25
    • Weber, C.1
  • 95
    • 0016057704 scopus 로고
    • Maxwell's boundary value problem on Riemannian manifolds with nonsmooth boundaries
    • Weck, N. (1974). Maxwell's boundary value problem on Riemannian manifolds with nonsmooth boundaries. J. Math. Anal. Appl. 46, 410-437.
    • (1974) J. Math. Anal. Appl. , vol.46 , pp. 410-437
    • Weck, N.1
  • 96
    • 0001709606 scopus 로고
    • Über die asymptotische Verteilung der Eigenwerte
    • Weyl, H. (1911). Über die asymptotische Verteilung der Eigenwerte. Gott. Nach. 110-117.
    • (1911) Gott. Nach. , pp. 110-117
    • Weyl, H.1
  • 97
    • 84871436168 scopus 로고
    • Über das Spectrum der Hohlraumstrahlung
    • Weyl, H. (1912). Über das Spectrum der Hohlraumstrahlung. J. Keine Angew. Math. 141, 163-181.
    • (1912) J. Keine Angew. Math. , vol.141 , pp. 163-181
    • Weyl, H.1
  • 98
    • 0003186296 scopus 로고
    • Kapazität von Strahlungsfeldern
    • Weyl, H. (1952). Kapazität von Strahlungsfeldern. Math. Z. 55, 187-198.
    • (1952) Math. Z. , vol.55 , pp. 187-198
    • Weyl, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.