Minkowski problem of anisotropic p-torsional rigidity

TL;DR

This paper investigates the Minkowski problem related to anisotropic p-torsional rigidity, establishing existence conditions and solving the log-Minkowski problem without symmetry assumptions in the anisotropic setting.

Contribution

It provides necessary and sufficient conditions for solutions and addresses the existence of solutions to the log-Minkowski problem without symmetry assumptions.

Findings

Established conditions for the existence of solutions.

Solved the log-Minkowski problem without symmetry assumptions.

Extended Minkowski problem theory to 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.