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arXiv · 2605.19504

A regularity result for $BV^{\mathcal{A}}(\Omega)$

Jakob Deutsch·Samuele Riccò
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Abstract

It is well known that distributions whose symmetrized gradient is a bounded Radon measure belong to the space $BD$ on bounded domains with $\mathcal{C}^1$ boundary. In this work, we extend this result to a broader class of first-order linear elliptic operators. More precisely, let $\mathcal{A}$ be a first-order linear elliptic operator satisfying the rank-one property. We prove that if a distribution defined on a Lipschitz domain has bounded $\mathcal{A}$-variation, then it belongs to the space $BV^{\mathcal{A}}$.

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Jakob Deutsch, Samuele Riccò. 2026-05-19. A regularity result for $BV^{\mathcal{A}}(\Omega)$. https://arxiv.org/abs/2605.19504

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