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arXiv · 1711.11369

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

Nikolai Ubostad
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Abstract

The boundary regularity for the normalized $p$-parabolic equation $u_t =\frac{1}{p}|Du|^{2-p}\Delta_pu$ 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 $p \to \infty$.

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Nikolai Ubostad. 2017-11-30. On the normalized $p$-parabolic equation in arbitrary domains. https://arxiv.org/abs/1711.11369

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