(L^p\) regularity of least gradient functions

It is shown that solutions to the anisotropic least gradient problem for boundary data \(f \in L^p(\partial\Omega)\) lie in \(L^{\frac{Np}{N-1}}(\Omega)\); the exponent is shown to be optimal. Moreover, the solutions are shown to be locally bounded with explicit bounds on the rate of blow-up of the...

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Bibliographic Details
Published in:arXiv.org 2019-04
Main Author: Górny, Wojciech
Format: Article
Language:English
Subjects:
Anisotropy
Online Access:Get full text
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Summary:It is shown that solutions to the anisotropic least gradient problem for boundary data \(f \in L^p(\partial\Omega)\) lie in \(L^{\frac{Np}{N-1}}(\Omega)\); the exponent is shown to be optimal. Moreover, the solutions are shown to be locally bounded with explicit bounds on the rate of blow-up of the solution near the boundary in two settings: in the anisotropic case on the plane and in the isotropic case in any dimension.
ISSN:2331-8422