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

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arxiv 1806.01921 v1 pith:3CH5ADYO submitted 2018-06-05 math.AP

Wojciech Górny This is my paper · ORCID
classification math.AP
keywords convexgradientleastminimizersnormomegaproblemregularity
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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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  1. Least gradient problem on annuli

    math.AP 2019-08 conditional novelty 6.0 of 10

    For annuli in the plane, the BV least gradient problem with BV boundary data is shown to be equivalent to a boundary-to-boundary optimal transport problem, and under admissibility conditions a unique solution with W^{...

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