Mathematical Research Letters

Volume 30 (2023)

Number 5

On $\infty$-ground states in the plane

Pages: 1565 – 1589

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n5.a11

Authors

Erik Lindgren (Department of Mathematics, Uppsala University, Uppsala, Sweden)

Peter Lindqvist (Department of Mathematical Sciences, Norwegian University of Science and Technology, Trondheim, Norway)

Abstract

We study $\infty$-Ground states in convex domains in the plane. In a polygon, the points where an $\infty$-Ground state does not satisfy the $\infty$-Laplace Equation are characterized: they are restricted to lie on specific curves, which are acting as attracting (fictitious) streamlines. The gradient is continuous outside these curves and no streamlines can meet there.

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Erik Lindgren was supported by the Swedish Research Council, grant no. 2017-03736. Peter Lindqvist was supported by The Norwegian Research Council, grant no. 250070 (WaNP).

Received 29 March 2021

Received revised 3 June 2022

Accepted 25 June 2022

Published 14 May 2024