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arXiv · 2305.18876

Strongly anisotropic Anzellotti pairings and their applications to the anisotropic $p$-Laplacian

Wojciech Górny
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Abstract

In this paper, we study the parabolic and elliptic problems related to the anisotropic $p$-Laplacian operator in the case when it has linear growth on some of the coordinates. In order to define properly a notion of weak solutions and prove their existence, we first construct an anisotropic analogue of Anzellotti pairings and prove a weak Gauss-Green formula which relates the newly constructed pairing with a normal trace of a sufficiently regular vector field.

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Wojciech Górny. 2023-05-30. Strongly anisotropic Anzellotti pairings and their applications to the anisotropic $p$-Laplacian. https://arxiv.org/abs/2305.18876

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