Reaction-Diffusion in Nonsmooth and Closed DomainsReport as inadecuate

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Boundary Value Problems

, 2007:031261

Harnack-s Estimates, Positivity and Local Behavior of Degenerate and Singular Parabolic Equations


We investigate the Dirichlet problem for the parabolic equationOpen image in new window in a nonsmooth and closed domainOpen image in new window possibly formed with irregular surfaces and having a characteristic vertex point. Existence, boundary regularity, uniqueness, and comparison results are established. The main objective of the paper is to express the criteria for the well-posedness in terms of the local modulus of lower semicontinuity of the boundary manifold. The two key problems in that context are the boundary regularity of the weak solution and the question whether any weak solution is at the same time a viscosity solution.

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Author: Ugur G Abdulla


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