Gradient variational problems in R2

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Date
2022
Author(s)
Kenyon, Richard
Prause, István
Unique identifier
10.1215/00127094-2022-0036
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Citation
Kenyon, Richard. Prause, István. (2022). Gradient variational problems in R2.  Duke mathematical journal , 171 (14) , 3003-3022. 10.1215/00127094-2022-0036.
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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.

Keywords
inhomogeneous Laplace equation   surface tension   tiling   variational problem   
URI
https://erepo.uef.fi/handle/123456789/28965
Link to the original item
http://dx.doi.org/10.1215/00127094-2022-0036
Publisher
Duke University Press
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