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arXiv · 1503.06402

Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data

Tomasz Klimsiak
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Abstract

We consider the obstacle problem with irregular barriers for semilinear elliptic equation involving measure data and operator corresponding to a general quasi-regular Dirichlet form. We prove existence and uniqueness of a solution as well as its representation as an envelope of a supersolution to some related partial differential equation. We also prove regularity results for the solution and the Lewy-Stampacchia inequality.

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Tomasz Klimsiak. 2015-03-22. Quasi-regular Dirichlet forms and the obstacle problem for elliptic equations with measure data. https://arxiv.org/abs/1503.06402

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