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arXiv · 1303.4456

Parabolic equations in simple convex polytopes with time irregular coefficients

Hongjie Dong·Doyoon Kim
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Abstract

We prove the $W^{1,2}_p$-estimate and solvability for the Dirichlet problem of second-order parabolic equations in simple convex polytopes with time irregular coefficients, when $p\in (1,2]$. We also consider the corresponding Neumann problem in a half space when $p\in [2,\infty)$. Similar results are obtained for equations in a half space with coefficients which are measurable in a tangential direction and have small mean oscillations in the other directions.

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Hongjie Dong, Doyoon Kim. 2013-03-19. Parabolic equations in simple convex polytopes with time irregular coefficients. https://doi.org/10.1137/130936890

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