Extremal functions for an embedding from some anisotropic space, and partial differential equation involving the "one Laplacian"

Françoise Demengel; Thomas Dumas

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arXiv · 1804.06351

Extremal functions for an embedding from some anisotropic space, and partial differential equation involving the "one Laplacian"

Françoise Demengel·Thomas Dumas

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Abstract

In this paper, we prove the existence of extremal functions for the best constant of embedding from anisotropic space, allowing some of the Sobolev exponents to be equal to $1$. We prove also that the extremal functions satisfy a partial differential equation involving the $1$ Laplacian.

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Françoise Demengel, Thomas Dumas. 2018-04-17. Extremal functions for an embedding from some anisotropic space, and partial differential equation involving the "one Laplacian". https://arxiv.org/abs/1804.06351

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