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RESEARCH PRODUCT

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

Anders BjörnJana BjörnMikko Parviainen

subject

Primary: 35K61 Secondary: 35B30 35B51 35D40 35K92Mathematics - Analysis of PDEsMathematics::Analysis of PDEsFOS: MathematicsAnalysis of PDEs (math.AP)

description

We study boundary regularity for the normalized $p\mspace{1mu}$-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970), 683-693) showed that the so-called tusk condition guarantees regularity for the heat equation. We generalize this result to the normalized $p\mspace{1mu}$-parabolic equation, and also obtain H\"older continuity. The tusk condition is a parabolic version of the exterior cone condition. We also obtain a sharp Petrovski criterion for the regularity of the latest moment of a domain. This criterion implies that the regularity of a boundary point is affected if one side of the equation is multiplied by a constant.

yearjournalcountryeditionlanguage
2017-12-19
https://dx.doi.org/10.48550/arxiv.1712.06807