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arXiv · 2606.17483

Existence and stability of solutions of the Dirichlet problem for the $p$-Poisson equation in metric measure spaces

Luis Castillo·Timo Takala
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Abstract

We study the Dirichlet problem for the $p$-Poisson equation in the metric measure space setting equipped with a doubling measure and supporting a $(p,p)$-Poincar\'e inequality. We prove the existence of the solutions by using a variational approach. We prove the stability and uniqueness of the solutions, when the space is also geodesic.

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Luis Castillo, Timo Takala. 2026-06-16. Existence and stability of solutions of the Dirichlet problem for the $p$-Poisson equation in metric measure spaces. https://arxiv.org/abs/2606.17483

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