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M. Goering (MPI MiS Leipzig): Finslerian regularity theory in Euclidean space

Ort: Oberseminar Analysis Augusteum A314

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. From here we discuss potential applications of our new techniques to create Finslerian analogs of classical theorems in geometric measure theory.

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Beginn: 30. Juni 2022 15:00

Ende: 30. Juni 2022 17:00