FALL 2020 Nonlinear Analysis Seminar Series

Dr. Adolfo Arroyo-Rabasa, University of Warwick

Title: Higher-integrability estimates for systems of PDEs with a non-linear pointwise elliptic constraint

Abstract:

I will discuss (L1,Lp) estimates for systems of PDEs of the form Au = 0, where A is a linear differential operator with constant coefficients and u is a vector-valued map satisfying a pointwise constraint of the form u(x) \in C, where C is a convex cone with sufficiently small aperture. I will collect some applications of this result to discuss higher integrability for Sobolev spaces and other spaces of bounded variation. This is joint work with G. De Philippis, J. Hirsch, F. Rindler and A. Skorobogatova.

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