Abstract for the talk on 29.09.2023 (11:00 h)
AG Analysis-ProbabilityGreta Marino (Universität Augsburg)
Lipschitz regularity for solutions of a general class of elliptic equations
29.09.2023, 11:00 h, MPI für Mathematik in den Naturwissenschaften Leipzig, E2 10 (Leon-Lichtenstein)
We prove local Lipschitz regularity for local minimisers of
\[W^{1,1}(\Omega)\ni v\mapsto \int_\Omega F(Dv)\, dx\]
where \(\Omega\subseteq \R^N\), \(N\ge 2\) and \(F:\R^N\to \R\) is a quasiuniformly convex integrand in the sense of [Kovalev and Maldonado, 2005], i.e.,a convex \(C^1\)-function such that the ratio between the maximum and minimum eigenvalues of \(D^2F\) is essentially bounded. This class of integrands includes the standard functions \(F(z)=|z|^p\) for any \(p>1\) and arises as the closure, with respect to a natural convergence, of the strongly elliptic integrands of the Calculus of Variations.