Smoothness up to the free boundary for the $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow

Albert Chau; Ben Weinkove

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arXiv · 2412.10144

Smoothness up to the free boundary for the $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow

Albert Chau·Ben Weinkove

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Abstract

The $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow with a flat side are degenerate parabolic equations with evolving free boundaries. We give proofs of smooth short-time existence, up to the free boundaries, using a result of the authors on linear degenerate equations on a fixed domain.

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Albert Chau, Ben Weinkove. 2024-12-13. Smoothness up to the free boundary for the $p$-Laplacian evolution equation and the $\alpha$-Gauss curvature flow. https://arxiv.org/abs/2412.10144

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