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