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arXiv · 1712.07150

The planar Least Gradient problem in convex domains

Piotr Rybka·Ahmad Sabra
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Abstract

We study the two dimensional least gradient problem in a convex, but not necessary strictly convex region. We look for solutions in the space of $BV$ functions satisfying the boundary data $f$ in trace sense. We assume that $f$ is in $BV$ too. We state admissibility conditions on the trace and on the domain that are sufficient for existence of solutions.

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Piotr Rybka, Ahmad Sabra. 2017-12-19. The planar Least Gradient problem in convex domains. https://arxiv.org/abs/1712.07150

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