On the normalized $p$-parabolic equation in arbitrary domains

Abstract

The boundary regularity for the normalized $p$-parabolic equation $u_t=\frac{1}{p}|Du{|}^{2-p}{\Delta }_{p}u$ is studied. Perron's method is used to construct solutions in arbitrary domains. We classify the regular boundary points in terms of barrier functions, and prove an Exterior Sphere result. A fundamental solution is identified. A Petrovsky criterion is established, and we examine the convergence of solutions as $p\to \infty$.

References in corpus (1)

• The tusk condition and Petrovski criterion for the normalized $p\mspace{1mu}$-parabolic equation

Cited by in corpus (1)

• The tusk condition and Petrovski criterion for the normalized $p\mspace{1mu}$-parabolic equation