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arXiv · 2601.23195

Non-uniformly elliptic variational problems on BV

Lisa Beck·Franz Gmeineder·Mathias Schäffner
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Abstract

We establish $\mathrm{W}^{1,1}$-regularity and higher gradient integrability for relaxed minimizers of convex integral functionals on $\mathrm{BV}$. Unlike classical examples such as the minimal surface integrand, we only require linear growth from below but not necessarily from above. This typically comes with a non-uniformly degenerate elliptic behaviour, for which our results extend the presently available bounds from the superlinear growth case in a sharp way.

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Lisa Beck, Franz Gmeineder, Mathias Schäffner. 2026-01-30. Non-uniformly elliptic variational problems on BV. https://arxiv.org/abs/2601.23195

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