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arXiv · 1806.01921

Least gradient problem with respect to a non-strictly convex norm

Wojciech Górny
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Abstract

We study the planar least gradient problem with respect to an anisotropic norm $\phi$ for continuous boundary data. We prove existence of minimizers for strictly convex domains $\Omega$. Furthermore, we inspect the issue of uniqueness and regularity of minimizers only in terms of the modes of convexity of $\phi$ and $\Omega$. The results are independent from the regularity of $\phi$.

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Wojciech Górny. 2018-06-05. Least gradient problem with respect to a non-strictly convex norm. https://arxiv.org/abs/1806.01921

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