Minkowski problem of anisotropic p-torsional rigidity

Abstract

In this paper, we consider the Minkowski problem associated with the solution to the anisotropic $p$-Laplacian (or Finsler $p$-Laplacian) equation, namely, the Minkowski problem of anisotropic $p$-torsional rigidity. The sufficient and necessary conditions for the existence of a solution to the Minkowski problem of anisotropic $p$-torsional rigidity are presented. Meanwhile, the existence of a solution to the log-Minkowski problem of anisotropic $p$-torsional rigidity without symmetry assumptions is solved.