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arXiv · 1311.5955

The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces

Daniel Hansevi
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Abstract

We study the obstacle problem for unbounded sets in a proper metric measure space supporting a (p,p)-Poincare inequality. We prove that there exists a unique solution. We also prove that if the measure is doubling and the obstacle is continuous, then the solution is continuous, and moreover p-harmonic in the set where it does not touch the obstacle. This includes, as a special case, the solution of the Dirichlet problem for p-harmonic functions with Sobolev type boundary data.

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Daniel Hansevi. 2013-11-23. The obstacle and Dirichlet problems associated with p-harmonic functions in unbounded sets in Rn and metric spaces. https://doi.org/10.5186/aasfm.2015.4005

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