The Infinity-Potential in the Square

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.

24 pages, 4 figures