Mathematics > Analysis of PDEs
arXiv:2606.17483 (math)
[Submitted on 16 Jun 2026]
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 $(p,p)$-Poincaré 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.
Submission history
From: Timo Takala [view email]
[v1]
Tue, 16 Jun 2026 03:50:09 UTC (16 KB)
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