Finslerian regularity theory in Euclidean space

Abstract: In the setting of sets of finite perimeter, the regularity of surfaces minimizing $\| \cdot \|_{p}$-surface energies is entirely unknown. Since these energies do not satisfy Almgren's ellipticity condition, the PDE that arises (as the partial linearization in the small gradient regime of the anisotropic minimal surface) is very degenerate elliptic. In this example, the relevant PDE is the Finsler $\gamma$-Laplacian. This motivates a discussion of the state-of-the-art regularity theory for the very degenerate elliptic and non-linear Finsler $\gamma$-Laplacian. Pending time, some potential applications to classical questions in geometric measure theory will also be discussed. This talk discusses joint work.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdifferential geometryfunctional analysismetric geometrynumerical analysisoptimization and control

Audience: researchers in the topic

Online Seminar "Geometric Analysis"

Series comments: We discuss recent trends related to geometric analysis in a broad sense. The general idea is to solve geometric problems by means of advanced tools in analysis. We will include a wide range of topics such as geometric flows, curvature functionals, discrete differential geometry, and numerical simulation.

Registration and links to videos available at blatt.sbg.ac.at/onlineseminar.php