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- W4287723758 abstract "We study the two dimensional least gradient problem in convex polygonal sets in the plane, $Omega$. We show the existence of solutions when the boundary data $f$ are attained in the trace sense. The main difficulty here is a possible discontinuity of $f$. Moreover, due to the lack of strict convexity of $Omega$, the classical results are not applicable. We state the admissibility conditions on the boundary datum $f$, that are sufficient for establishing an existence result. One of them is that $fin BV(partialOmega)$. The solutions are constructed by a limiting process, which uses solutions to known problems" @default.
- W4287723758 created "2022-07-26" @default.
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- W4287723758 date "2020-07-13" @default.
- W4287723758 modified "2023-10-16" @default.
- W4287723758 title "The planar Least Gradient problem in convex domains: the discontinuous case" @default.
- W4287723758 doi "https://doi.org/10.48550/arxiv.2007.06361" @default.
- W4287723758 hasPublicationYear "2020" @default.
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