标题： 关于各向异性p-扭转刚度的闵可夫斯基问题 显示英文标题

标题： Minkowski problem of anisotropic p-torsional rigidity

摘要： 本文考虑了与各向异性$p$-Laplace（或Finsler$p$-Laplace）方程解相关的Minkowski问题，即各向异性$p$-扭转刚度的Minkowski问题。 给出了各向异性$p$-扭转刚度Minkowski问题解的存在性充分必要条件。 同时，在没有对称假设的情况下解决了各向异性$p$-扭转刚度对数Minkowski问题解的存在性。 显示英文摘要

摘要： 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 anisotropic $p$-torsional rigidity Minkowski problem are presented. Meanwhile, the existence of a solution to the log-Minkowski problem of anisotropic $p$-torsional rigidity without symmetry assumptions is solved.