On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:260

Article

Abdulla, UG

关键词: Dirichlet problem;    non-smooth domains;    nonlinear diffusion;    degenerate and singular parabolic equations;    boundary regularity;   

DOI  :  10.1006/jmaa.2001.7458

来源: Elsevier

【 摘 要 】

We study the Dirichlet problem for the parabolic equation u(t) = Deltau(m), m > 0, in a bounded, non-cylindrical and non-smooth domain Ohm subset of RN+1, N greater than or equal to 2. 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) Holder condition on it plays a crucial role for the boundary continuity of the constructed solution. The Holder exponent 1/2 is critical as in the, classical theory of the one-dimensional heat equation u(t) = u(xx). (C) 2001 Academic Press.

【 授权许可】

Free