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arXiv · 1211.0081

On elliptic equations in a half space or in convex wedges with irregular coefficients

Hongjie Dong
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Abstract

We consider second-order elliptic equations in a half space with leading coefficients measurable in a tangential direction. We prove the $W^2_p$-estimate and solvability for the Dirichlet problem when $p\in (1,2]$, and for the Neumann problem when $p\in [2,\infty)$. We then extend these results to equations with more general coefficients, which are measurable in a tangential direction and have small mean oscillations in the other directions. As an application, we obtain the $W^2_p$-solvability of elliptic equations in convex wedge domains or in convex polygonal domains with discontinuous coefficients.

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Hongjie Dong. 2012-11-01. On elliptic equations in a half space or in convex wedges with irregular coefficients. https://doi.org/10.1016/j.aim.2013.02.004

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