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arXiv · 2206.02697

Convergence and local-to-global results for $p$-superminimizers on quasiopen sets

Anders Björn·Jana Björn·Visa Latvala
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Abstract

In this paper, several convergence results for fine $p$-(super)minimizers on quasiopen sets in metric spaces are obtained. For this purpose, we deduce a Caccioppoli-type inequality and local-to-global principles for fine $p$-(super)minimizers on quasiopen sets. A substantial part of these considerations is to show that the functions belong to a suitable local fine Sobolev space. We prove our results for a complete metric space equipped with a doubling measure supporting a $p$-Poincar\'e inequality with $1<p< \infty$. However, most of the results are new also for unweighted $\mathbf{R}^n$.

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Anders Björn, Jana Björn, Visa Latvala. 2022-06-06. Convergence and local-to-global results for $p$-superminimizers on quasiopen sets. https://doi.org/10.1016/j.jde.2023.05.009

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