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Bibliographie
[An]Ancona, A., Communication personnelle, 1994.
[Ca]Carleson, L.,Selected Problems on Exceptional Sets, Van Nostrand, Princeton, N. J., 1967.
[FGS]Fabes, E. B., Garofalo, N. andSalsa, S., A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations,Illinois J. Math. 30 (1986), 536–565.
[Fa]Falconer, K.,Fractal Geometry, Mathematical Foundations and Applications, J. Wiley & Sons Ltd., New York, 1990.
[He1]Heurteaux, Y., Inégalités de Harnack à la frontière pour des opérateurs paraboliques,Thèse, Paris 11, 1989.
[He2]Heurteaux, Y., Solutions positives et mesure harmonique pour des opérateurs paraboliques dans des ouverts “lipschitziens”,Ann. Inst. Fourier (Grenoble) 41 (1991), 601–649.
[KW1]Kaufman, R. andWu, J. M., Parabolic potential theory,J. Differential Equations 43 (1982), 204–234.
[KW2]Kaufman, R. andWu, J. M., Parabolic measure on domains of class Lip 1/2,Compositio Math. 65 (1988), 201–207.
[KW3]Kaufman, R. andWu, J. M., Dirichlet problem of heat equation forC 2 domains,J. Differential Equations 80 (1989), 14–31.
[Ke]Kemper, J. T., Temperatures in several variables: kernel functions, representations and parabolic boundary values,Trans. Amer. Math. Soc. 167 (1972), 243–262.
[LM1]Lewis, J. L. andMurray, M. A. M., Regularity properties of commutators and layer potentials associated to the heat equation,Trans. Amer. Math. Soc. 328 (1991), 815–842.
[LM2]Lewis, J. L. andMurray, M. A. M., Absolute continuity of parabolic measures, inPartial Differential Equations with Minimal Smoothness and Applications (Dahlberg, B., Fabes, E., Fefferman, R., Jerison, D. and Kenig, C., eds.) IMA Vol. Math. Appl.42, pp. 173–188, Springer-Verlag, New York, 1992.
[LM3]Lewis, J. L. andMurray, M. A. M., The method of layer potentials for the heat equation in time-varying domains,Mem. Amer. Math. Soc. 545 (1995).
[LS]Lewis, J. L. andSilver, J., Parabolic measure and the Dirichlet problem for the heat equation in two dimensions,Indiana Univ. Math. J. 37 (1988), 801–839.
[Ni]Nishio, M., Uniqueness of positive solutions of the heat equation,Osaka J. Math. 29 (1992), 531–538.
[St]Stein, E. M.,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N. J., 1970.
[TW]Taylor, S. J. andWatson, N. A., A Hausdorff measure classification of polar sets for the heat equation,Math. Proc. Cambridge Philos. Soc. 97 (1985), 325–344.
[To]Torchinsky, A.,Real-variable Methods in Harmonic Analysis, Academic Press, Orlando, Fla., 1986.
[Wu1]Wu, J. M., On parabolic measures and subparabolic functions,Trans. Amer. Math. Soc. 251 (1979), 171–186.
[Wu2]Wu, J. M., On heat capacity and parabolic measure,Math. Proc. Cambridge Philos. Soc. 102 (1987), 163–172.
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Heurteaux, Y. Mesure harmonique et équation de la chaleur. Ark. Mat. 34, 119–139 (1996). https://doi.org/10.1007/BF02559511
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DOI: https://doi.org/10.1007/BF02559511