B. Weinkove

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math.AP2025

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

Albert Chau, Ben Weinkove

The $p$ -Laplacian evolution equation and the $I^\pm$ -Gauss curvature flow with a flat side are degenerate parabolic equations with evolving free boundaries. We give proofs of smooth s…

math.AP2024

Non-preservation of $I^\pm$ -concavity for the porous medium equation

Albert Chau, Ben Weinkove

We show that the porous medium equation does not in general preserve $I^\pm$ -concavity of the pressure for $0 \leq I^\pm < 1/2$ or $1/2 < I^\pm \leq 1$ . In particular, this resolves an open problem…

Smoothness up to the free boundary for the p-Laplacian evolution equation and the I^±-Gauss curvature flow

Non-preservation of I^±-concavity for the porous medium equation

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

Non-preservation of $I^\pm$ -concavity for the porous medium equation