The Infinity-Potential in the Square
Abstract
A representation formula for the solution of the ∞-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 ∞-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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