Well-posedness of the Dirichlet Problem for the Nonlinear Diffusion Equation in Non-smooth Domains
Ugur G. Abdulla
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Submission date: 05. Jun. 2000
published in: Transactions of the American Mathematical Society, 357 (2005) 1, p. 247-265
DOI number (of the published article): 10.1090/S0002-9947-04-03464-6
MSC-Numbers: 35K65, 35K55
Keywords and phrases: dirichlet problem, non-smooth domains, nonlinear diffusion, degenerate and singular parabolic equations, uniqueness and comparison results, l1-contraction, boundary gradient estimates
We investigate the Dirichlet problem for the parablic equation
in a non-smooth domain . In a recent paper  existence and boundary regularity results were established. In this paper we present uniqueness and comparison theorems and results on the continuous dependence of the solution on the initial-boundary data. In particular, we prove -contraction estimation in general non-smooth domains.