SPRING 2021 Nonlinear Analysis Seminar Series

Professor Jan Kristensen,  University of Oxford

Title: Regularity and uniqueness results in some variational problems

Abstract:

It is known that minimizers of strongly polyconvex variational integrals need not be regular nor unique. However, if a suitable Gårding type inequality is assumed for the variational integral, then both regularity and uniqueness of minimizers can be restored under natural smallness conditions on the data. In turn, the Gårding inequality turns out to always hold under an a priori \(C^{1}\) regularity hypothesis on the minimizer, while its validity is not known in the general case. In this talk, we discuss these issues and how they are naturally connected to convexity of the variational integral on the underlying Dirichlet classes.
Part of the talk is based on ongoing joint work with Judith Campos Cordero, Bernd Kirchheim and Jan Kolar.

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