The initial-boundary value problems for the heat operator in non-cylindrical domains

Hisako WATANABE

doi:10.2969/jmsj/04930399

Hisako WATANABE

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JOURNAL FREE ACCESS

1997 Volume 49 Issue 3 Pages 399-430

DOI https://doi.org/10.2969/jmsj/04930399

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Published: 1997 Received: December 20, 1993 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: SUBTITLE Details: Wrong : Dedicated to Professor M. Nakai on the occasion of his 60th birthday

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : Ba) H. Bauer, Harmonische Räume und ihre Potentialtheorie, Lecture Notes in Math., 22, Springer, Berlin-Heidelberg-New York-Tokyo, 1966.
Br1) R. M. Brown, The method of layer potentials for the heat equation in Lipschitz cylinders, Amer. J. Math., 111 (1989), 339-379.
Br2) R. M. Brown, The initial-Neumann problem for the heat equation in Lipschitz cylinders, Trans. Amer. Math. Soc., 320 (1990), 1-52.
EG) L. C. Evans and R. F. Gariepy, Wiener's criterion for the heat equation, Arch. Rational Mech. Anal., 78 (1982), 293-314.
FGL) E. B. Fabes, N. Garofalo and E. Lanconelli, Wiener's criterion for divergence form parabolic operators with C¹-Dini continuous coefficients, Duke Math. J., 59 (1989), 191-232.
FR) E. B. Fabes and N.M. Rivière, Dirichlet and Neumann problems for the heat equation in C¹ cylinder, Proc. Sympos. Pure Math., 35 (1979), 179-196.
FS) E. B. Fabes and S. Salsa, Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders, Trans. Amer. Math. Soc., 279 (1983), 635-650.
Fr) A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, New York, 1964.
GL) N. Garofalo and E. Lanconelli, Wiener's criterion for parabolic equations with variable coefficients and its consequences, Trans. Amer. Math. Soc., 308 (1988), 811-836.
KW) R. Kaufman and J.-M. Wu, Dirichlet problem of heat equation for C² domains, J. Differential Equations, 80 (1989), 14-31.
L) E. Lanconelli, Sul problema di Dirichlet per l'equazione del calore, Ann. Mat. Pura Appl., 97 (1973), 83-114.
S) E. M. Stein, Singular integrals and differentiability properties of functions, Princeton, New Jersey, 1970.

Right : [Ba] H. Bauer, Harmonische Räume und ihre Potentialtheorie, Lecture Notes in Math., 22, Springer, Berlin-Heidelberg-New York-Tokyo, 1966.
[Br1] R. M. Brown, The method of layer potentials for the heat equation in Lipschitz cylinders, Amer. J. Math., 111 (1989), 339-379.
[Br2] R. M. Brown, The initial-Neumann problem for the heat equation in Lipschitz cylinders, Trans. Amer. Math. Soc., 320 (1990), 1-52.
[EG] L. C. Evans and R. F. Gariepy, Wiener's criterion for the heat equation, Arch. Rational Mech. Anal., 78 (1982), 293-314.
[FGL] E. B. Fabes, N. Garofalo and E. Lanconelli, Wiener's criterion for divergence form parabolic operators with C¹-Dini continuous coefficients, Duke Math. J., 59 (1989), 191-232.
[FR] E. B. Fabes and N. M. Rivière, Dirichlet and Neumann problems for the heat equation in C¹ cylinder, Proc. Sympos. Pure Math., 35 (1979), 179-196.
[FS] E. B. Fabes and S. Salsa, Estimates of caloric measure and the initial-Dirichlet problem for the heat equation in Lipschitz cylinders, Trans. Amer. Math. Soc., 279 (1983), 635-650.
[Fr] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, New York, 1964.
[GL] N. Garofalo and E. Lanconelli, Wiener's criterion for parabolic equations with variable coefficients and its consequences, Trans. Amer. Math. Soc., 308 (1988), 811-836.
[KW] R. Kaufman and J. -M. Wu, Dirichlet problem of heat equation for C² domains, J. Differential Equations, 80 (1989), 14-31.
[L] E. Lanconelli, Sul problema di Dirichlet per l'equazione del calore, Ann. Mat. Pura Appl., 97 (1973), 83-114.
[S] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton, New Jersey, 1970.

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