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arXiv · 2610.14321

The Liouville property for entire local minimizers from the space $BV_{\mathrm{loc}}(\R^2,\R^N)$ of variational integrals with linear growth

Michael Bildhauer·Martin Fuchs
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Abstract

We consider functions $u : \R^2 \rightarrow \R^N$ from the class $\Bloc$ which locally minimize the relaxed version of a variational integral with a strictly convex density being in addition of linear growth. It turns out that the boundedness of entire local minimizers $u$ implies their constancy.

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Michael Bildhauer, Martin Fuchs. 2026-10-09. The Liouville property for entire local minimizers from the space $BV_{\mathrm{loc}}(\R^2,\R^N)$ of variational integrals with linear growth. https://arxiv.org/abs/2610.14321

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