The Infinity-Potential in the Square

Karl K. Brustad

The Infinity-Potential in the Square

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arxiv 2210.03447 v2 pith:RJUXFXTY submitted 2022-10-07 math.AP

Karl K. Brustad This is my paper · ORCID

classification math.AP

keywords equationformulainftysquareappearsboundarycentreconjecture

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abstract

A representation formula for the solution of the $\infty$-Laplace equation is constructed in a punctured square, the prescribed boundary values being $u=0$ on the sides and $u=1$ at the centre. This so-called $\infty$-potential is obtained with a hodograph method. The heat equation is used and one of Jacobi's Theta functions appears. The formula disproves a conjecture.

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Infinity-harmonic functions and inverse mean curvature flow clusters
math.AP 2026-07 accept novelty 8.0 of 10

Infinity-harmonic functions on planar domains are C^{1,1/3} with isolated critical points and unique quasiradial blow-ups, via a p-to-infinity duality that produces inverse mean curvature flow clusters.

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