On the Dirichlet Problem for the Nonlinear Diffusion Equation in Non-smooth Domains

Ugur G. Abdulla

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Submission date: 31. Aug. 2001
Pages: 37
published in: Journal of mathematical analysis and applications, 260 (2001) 2, p. 384-403 
DOI number (of the published article): 10.1006/jmaa.2001.7458
Bibtex
MSC-Numbers: 35K65, 35K55
Keywords and phrases: dirichlet problem, non-smooth domains, nonlinear diffusion, degenerate and singular parabolic equations, boundary regularity
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Abstract:
We study the Dirichlet problem for the parabolic equation

in a bounded, non-cylindrical and non-smooth domain . Existence and boundary regularity results are established. We introduce a notion of parabolic modulus of left-lower (or left-upper) semicontinuity at the points of the lateral boundary manifold and show that the upper (or lower) Hölder condition on it plays a crucial role for the boundary continuity of the constructed solution. The Hölder exponent is critical as in the classical theory of the one-dimensional heat equation .

This research was supported by the Alexander von Humboldt Foundation.Download paper published in Journal of Mathematical Analysis and Applications