Work

The infinity-potential in the square

Year: 2025

Type: article

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 {u=0} on the sides and u = 1 {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.

Source: Advances in Calculus of Variations

DOI: 10.1515/acv-2025-0020

Author: Karl K. Brustad

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,712

Funder: Vetenskapsrådet

Award: Institut Mittag-Leffler