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arXiv · 1605.00035

Special cases of the planar least gradient problem

Wojciech Górny·Piotr Rybka·Ahmad Sabra
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Abstract

We study two special cases of the planar least gradient problem. In the first one, the boundary conditions are imposed on a part of the strictly convex domain. In the second case, we impose the Dirichlet data on the boundary of a rectangle, an example of convex but not strictly convex domain. We show the existence of solutions and study their properties for particular cases of data.

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Wojciech Górny, Piotr Rybka, Ahmad Sabra. 2016-04-29. Special cases of the planar least gradient problem. https://arxiv.org/abs/1605.00035

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