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Varopoulos, N. Th. Gaussian Estimates in Lipschitz Domains. Canadian journal of mathematics, Tome 55 (2003) no. 2, pp. 401-431. doi: 10.4153/CJM-2003-018-9
@article{10_4153_CJM_2003_018_9,
author = {Varopoulos, N. Th.},
title = {Gaussian {Estimates} in {Lipschitz} {Domains}},
journal = {Canadian journal of mathematics},
pages = {401--431},
year = {2003},
volume = {55},
number = {2},
doi = {10.4153/CJM-2003-018-9},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2003-018-9/}
}
[1] [1] Aronson, D. G., Non negative solutions of linear parabolic equations. Ann. Scuola Norm. Sup. Pisa 22 (1968), 607–694. Google Scholar
[2] [2] Bass, R. F. and Burdzy, K., A boundary Harnack principle in twisted Hçlder domains. Ann. of Math. (134) 134 (1991), 253–276. Google Scholar
[3] [3] Bass, R. F. and Burdzy, K., The boundary Harnack principle for nondivergence form elliptic operators. J. LondonMath. Soc. (2) 50 (1994), 157–169. Google Scholar
[4] [4] Bauman, P., Positive solutions of elliptic equations in nondivergence form and their adjoints. Ark. Mat. 22 (1984), 153–173. Google Scholar
[5] [5] Bauman, P., A Wiener test for nondivergence structure, second-order elliptic equations. Indiana Univ. Math. J. 34 (1985), 825–844. Google Scholar
[6] [6] Bensoussan, A., Lions, J.-L. and Papanicolaou, G. C., Asymptotic Analysis of Periodic Structures. North-Holland Publ., 1978. Google Scholar
[7] [7] Calderon, A. P., Lebesgue spaces of differentiable functions and distributions. Proc. Sympos. Pure Math. 5 (1961), 33–49. Google Scholar
[8] [8] Carleson, L., On the existence of boundary values for harmonic functions in several variables. Ark. Mat. 4 (1962), 339–393. Google Scholar
[9] [9] Carne, T. K., A transmutation formula for Markov chains. Bull. Sci. Math. (2) 109 (1985), 399–405. Google Scholar
[10] [10] Chung, S. Y. A., Wilson, J. M. and Wolf, T. H., Some weighted norm inequalities concerning the Schrçdinger Operator. Comm. Math. Helv. 60 (1985), 217–246. Google Scholar
[11] [11] Saloff-Coste, L., A note on Poincaré Sobolev and Harnack inequalities. Duke Math. J. IMRN 2 (1992), 27–28. Google Scholar
[12] [12] Delmotte, T., Parabolic Harnack inequality and estimates of Markov chains on graphs. Rev. Mat. Iberoamericana (1) 15 (1999), 181–232. Google Scholar
[13] [13] Doob, J. L., Classical Potential Theory and its Probabilistic Counterpart. Springer-Verlag. Google Scholar
[14] [14] Doob, J. L., Stochastic Processes. J. Wiley. Google Scholar
[15] [15] Fabes, E. B., Garofalo, N. and Salsa, , A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations. Illinois J. Math. 30 (1986), 536–565. Google Scholar
[16] [16] Fabes, E. and Safonov, M. V., Behavior near the boundary of positive solutions of second order parabolic equations. J. Fourier Anal. Appl. 3 (1997), 871–882. Google Scholar
[17] [17] Fabes, E. B., Safonov, M. V. and Yuan, Y., Behavior near the boundary of positive solutions of second order parabolic equations. II. Trans. Amer.Math. Soc. (12) 351 (1999), 4947–4961. Google Scholar
[18] [18] Fabes, E., Garofalo, N., Marin-Malava, S. and Salsa, S., Fatou theorems for some nonlinear elliptic equations. Rev. Mat. Iberoamericana (2) 4 (1988), 227–251. Google Scholar
[19] [19] Fabes, E. B. and Stroock, D., The Lp-integrability of Green's functions and fundamental solutions for elliptic and parabolic equations. Duke Math. J. 51 (1984), 977–1016. Google Scholar
[20] [20] Fabes, E. B. and Stroock, D., A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash. Arch. Rational Mech. Anal. (4) 96 (1986), 327–338. Google Scholar
[21] [21] Fukushima, M., Dirichlet forms and Marlov Processes. North-Holland, 1980. Google Scholar
[22] [22] Feller, W., An Introduction to Probability Theory. Volumes I and II, Wiley. Google Scholar
[23] [23] Garofalo, N., Second order parabolic equations in nonvariational forms: boundary Harnack principle and comparison theorems for nonnegative solutions. Ann.Mat. Pura Appl. 138 (1984), 367–296. Google Scholar
[24] [24] Grigoryan, A., Gaussian upper bounds for the heat kernel on arbitrary manifolds. J. Differential Geom. 45 (1997), 33–52. Google Scholar
[25] [25] Hebisch, W., Saloff-Coste, L.. Gaussian estimates for Markov chains and random walks on groups. Ann. Probab. (2) 21 (1993), 673–709. Google Scholar
[26] [26] Jerison, D. and Kenig, C., Boundary behaviour of harmonic functions in nontangentially accessible domains. Adv. in Math. 146 (1982), 80–147. Google Scholar
[27] [27] Kenig, C. E., Potential Theory of Non-Divergence Form Elliptic Equations. Proceedings of C.I.M.E. Course in Dirichlet forms, 1992. Google Scholar
[28] [28] Kenig, C. E., Harmonic analysis techniques for second order elliptic boundary value problems. C.B.M.S. 83, Amer.Math. Soc., 1994. Google Scholar
[29] [29] Krylov, N. V. and Safonov, M. V., A property of the solutions of parabolic equations with measurable coefficients. Izv. Akad. Nauk SSSR 44, English Translation Math. USSR-Izv. 16 (1981), 151–164. Google Scholar
[30] [30] Kuo, H.-J. and Trudinger, N. S., Evolving monotone difference operators on general space-time meshes. Duke Math. J. (3) 91 (1998), 587–607. Google Scholar
[31] [31] Lawler, G. F., Estimates for differences and Harnack inequality for difference operators coming from random walks with symmetric, spatially inhomogeneous, increments. Proc. LondonMath. Soc. (3) 63 (1991), 552–568. Google Scholar
[32] [32] Mackenhoupt, B., The equivalence of two conditions for weight functions. Studia Math. 49 (1974), 101–106. Google Scholar
[33] [33] McKean, H. P. Jr., Stochastic Integrals. Academic Press, 1969. Google Scholar
[34] [34] Moser, J., On Harnack's theorem for elliptic differential equations. Comm. Pure Appl. Math. 14 (1961), 557–591. Google Scholar
[35] [35] Moser, J., A Harnack inequality for parabolic differential equations. Comm. Pure and Appl. Math. 17 (1964), 101–134. Google Scholar
[36] [36] Moser, J., A Harnack inequality for parabolic differential equations. Comm. Pure Appl. Math. 20 (1967), 232–236. Google Scholar
[37] [37] Safonov, M. V. and Yuan, Y., Doubling properties for second order parabolic equations. Ann. of Math. 150 (1999), 313–327. Google Scholar
[38] [38] Stein, E. M., Singular Integrals and Differentiation Properties of Functions. Princeton Univ. Press. Google Scholar
[39] [39] Ušakov, V. I., Stabilization of solutions of the third mixed problem for a second-order parabolic equation in a noncylindrical domain. Mat. Sb. 153(1980), Translation: Math. USSR-Sb. (1) 39 (1981), 87–105. Google Scholar
[40] [40] Varopoulos, N. Th., Information theory and harmonic functions. Bull. Sci. Math. (2) 109 (1985), 225–252. Google Scholar
[41] [41] Varopoulos, N. Th., Isoperimetric inequalities and Markov chains. J. Funct. Anal. 63 (1985), 240–260. Google Scholar
[42] [42] Varopoulos, N. Th., Geometric and potential theoretic results on Lie groups. Canad. J. Math. (2) 52 (2000), 412–437. Google Scholar
[43] [43] Varopoulos, N. Th., Potential theory in Lipchitz domains. Canad. J. Math. (5) 53 (2001), 1057–1120. Google Scholar
[44] [44] Varopoulos, N. Th., Saloff-Coste, L. and T. Coulhon, Analysis and Geometry on Groups. Cambridge Tracts in Math. 100(1992). Google Scholar
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