$L^p$ regularity of least gradient functions

Wojciech Górny

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arXiv · 1904.11348

$L^p$ regularity of least gradient functions

Wojciech Górny

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Abstract

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.

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Wojciech Górny. 2019-04-24. $L^p$ regularity of least gradient functions. https://arxiv.org/abs/1904.11348

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