Caloric measure on domains bounded by Weierstrass-type graphs

Annales Academiae Scientiarum Fennicae Mathematica

Volumn 25, Issue 2, 2000, Pages 501-522

  Bousch, Thierry ^a   Heurteaux, Yanick ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034366502     PISSN: 1239629X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. [Ba] BATAKIS, A.: Harmonic measure of some Cantor type sets. - Ann. Acad. Sci. Fenn. Math. 21, 1996, 255-270.
2. [BH] BATAKIS, A., and Y. HEURTEAUX: On relations between entropy and Hausdorff di- mension of measures. - Preprint, Orsay, 1998.
3. [Bg] BOURGAIN, J.: On the Hausdorff dimension of harmonic measure in higher dimension. - Invent. Math. 87, 1987, 477-483.
4. [Bo] BOUSCH, T.: Le poisson n'a pas d'arêtes. - Preprint, 1998.
5. [BMP] BROWN, G., G. MICHON, and J. PEYRIÉRE: On the multifractal analysis of measures. - J. Stat. Phys. 66, 1992, 775-790.
6. [C] CARLESON, L.: On the support of harmonic measure for sets of Cantor type. - Ann. Acad. Sci. Fenn. Math. 10, 1985, 113-123.
7. [Da] DAHLBERG, B.: Estimates of harmonic measure. - Arch. Rational Mech. Anal. 65, 1977, 275-288.
8. [Do] DOOB, J.L.: Classical Potential Theory and its Probabilistic Counterpart. - Springer-Verlag, New York, 1984.
9. [FGS] FABES, E.B., N. GAROFALO, and S. SALSA: A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations. - Illinois J. Math. 30, 1986, 536-565.
10. [F] FALCONER, K.: Fractal Geometry. - Mathematical Foundations and Applications. John Wiley & Sons, New York, 1990.
11. [H1] HEURTEAUX, Y.: Inégalités de Harnack à la frontière pour des opérateurs paraboliques.- Ph.D. thesis, Université Paris-Sud, 1989.
12. [H2] HEURTEAUX, Y.: Solutions positives et mesure harmonique pour des opérateurs para-boliques dans des ouverts "lipschitziens". - Ann. Inst. Fourier (Grenoble) 41, 1991, 601-649.
13. [H3] HEURTEAUX, Y.: Sur la comparaison des mesures avec les mesures de Hausdorff. - C. R. Acad. Sci. Paris Sér. I Math. 321, 1995, 61-65.
14. [H4] HEURTEAUX, Y.: Mesure harmonique et équation de la chaleur. - Ark. Mat. 34, 1996, 119-139.
15. [H5] HEURTEAUX, Y.: Estimations de la dimension inférieure et de la dimension supérieure des mesures. - Ann. Inst. H. Poincaré Probab. Statist. 34, 1998, 309-338.
16. [KMPY] KAPLAN, J.L., J. MALLET-PARET, and J.A. YORKE: The Lyapunov dimension of a nowhere differentiate attracting torus. - Ergodic Theory Dynam. Systems 4, 1984, 261-281.
17. [KW] KAUFMAN, R., and J.M. WU: Parabolic measure on domains of class Lip 1/2. - Compositio Math. 65, 1988, 201-207.
18. [K] KEMPER, J.T.: Temperatures in several variables: kernel functions, representations and parabolic boundary values. - Trans. Amer. Math. Soc. 167, 1972, 243-262.
19. [LS] LEWIS, J.L., and J. SILVER: Parabolic measure and the Dirichlet problem for the heat equation in two dimensions. - Indiana Univ. Math. J. 37, 1988, 801-839.
20. [MV] MAKAROV, N., and A. VOLBERG: On the harmonic measure of discontinuous fractals. - Preprint LOMI E-6-86, Leningrad, 1986.
21. [Na] NAÏM, L.: Sur le rôle de la frontière de R.S. Martin dans la théorie du potentiel. - Ann. Inst. Fourier (Grenoble) 7, 1957, 183-281.
22. [Ny] NYSTRÖM, K.: The Dirichlet problem for second order parabolic operators. - Indiana Univ. Math. J. 46, 1997, 183-245.
23. [PU] PRZYTYCKI, F., and M. URBANSKI: On the Hausdorff dimension of some fractal sets. - Studia Math. 93, 1989, 155-186.
24. [TW] TAYLOR, S.J., and N.A. WATSON: A Hausdorff measure classification of polar sets for the heat equation. - Math. Proc. Cambridge Philos. Soc. 97, 1985, 325-344.
25. [W] Wu, J.M.: On parabolic measures and subparabolic functions. - Trans. Amer. Math. Soc. 251, 1979, 171-186.