Mathematical Analysis Seminars @ DISIM

Title: The black hole stability problem in general relativity

Abstract: Black holes are perhaps the most spectacular theoretical prediction of Einstein's theory of general relativity. A mathematical proof of their stability as solutions to the Einstein equations remains a fundamental open problem in the subject. The talk will outline the formulation, major difficulties, and implications of the problem, including its connections with recent advances in the experimental observation of these objects.

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Title: TBA

Abstract: TBA

Title: Quantitative vanishing viscosity approximation of fully nonlinear, non-convex, Hamilton-Jacobi equations with Hölder data.

Abstract: We discuss new quantitative estimates of the vanishing viscosity process for evolutionary Hamilton-Jacobi PDEs that are neither concave nor convex in the gradient and Hessian entries. I will describe a novel approach that exploits the regularizing properties of sup/inf-convolutions for viscosity solutions combined with the comparison principle. This method provides explicit sharp constants without assuming differentiability properties neither on solutions nor on the Hamiltonian. This is a joint work with Alekos Cecchin (Padova).