1 October 2022 Gradient variational problems in R2
Richard Kenyon, István Prause
Author Affiliations +
Duke Math. J. 171(14): 3003-3022 (1 October 2022). DOI: 10.1215/00127094-2022-0036

Abstract

We prove a new integrability principle for gradient variational problems in R2, showing that solutions are explicitly parameterized by κ-harmonic functions, that is, functions which are harmonic for the Laplacian with varying conductivity κ, where κ is the square root of the Hessian determinant of the surface tension.

Citation

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Richard Kenyon. István Prause. "Gradient variational problems in R2." Duke Math. J. 171 (14) 3003 - 3022, 1 October 2022. https://doi.org/10.1215/00127094-2022-0036

Information

Received: 2 April 2021; Revised: 10 September 2021; Published: 1 October 2022
First available in Project Euclid: 7 September 2022

MathSciNet: MR4491711
zbMATH: 1502.49003
Digital Object Identifier: 10.1215/00127094-2022-0036

Subjects:
Primary: 35C99 , 49Q10
Secondary: 82B20

Keywords: inhomogeneous Laplace equation , Surface tension , tiling , variational problem

Rights: Copyright © 2022 Duke University Press

Vol.171 • No. 14 • 1 October 2022
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