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arXiv · 1402.0036

The Dirichlet boundary problem for second order parabolic operators satisfying Carleson condition

Martin Dindoš·Sukjung Hwang
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Abstract

We establish $L^p$, $2\le p\le\infty$ solvability of the Dirichlet boundary value problem for a parabolic equation $u_t-\mbox{div}(A\nabla u)=0$ on time-varying domains with coefficient matrix $A=(a_{ij})$ that satisfy a small Carleson condition. The result is motivated by similar results for the elliptic equation $\mbox{div}(A\nabla u)=0$ that were established previously.

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Martin Dindoš, Sukjung Hwang. 2014-02-01. The Dirichlet boundary problem for second order parabolic operators satisfying Carleson condition. https://arxiv.org/abs/1402.0036

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