It is well known that several variational functionals verify Brunn- Minkowski type inequalities, such as: Torsional rigidity; First Dirichlet eigenvalue of the Laplace; p-Capacity... And their solutions of the corresponding boundary value problem (PDE's+boundary conditions), satisfy specific concavity properties. In this talk, I will present my recent work about the first Dirichlet eigenvalue problem to the weighted p-Laplace operator in Florence. (a joint work with Andrea Colesanti and Paolo Salani).

覃蕾，湖南大学数学学院博士生。主要从事于凸几何与偏微分方程方向的研究,主要聚焦于凸几何中的Minkowski问题研究以及椭圆型偏微分方程解的凹凸性及相应的Brunn-Minkowski不等式研究。其研究成果已在Adv. Math、Proc.AMS等杂志发表。