Gradient variational problems in \(\mathbb{R}^2\)

DOI10.1215/00127094-2022-0036zbMath1502.49003arXiv2006.01219OpenAlexW4294874092MaRDI QIDQ2081390

István Prause, Richard W. Kenyon

Publication date: 13 October 2022

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2006.01219

zbMATH Keywords

variational problemsurface tensiontilinginhomogeneous Laplace equation

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Optimization of shapes other than minimal surfaces (49Q10) Representations of solutions to partial differential equations (35C99) Existence theories for optimal control problems involving relations other than differential equations (49J21)

Related Items (5)

Conformal structure of autonomous Leray–Lions equations in the plane and linearisation by hodograph transform ⋮ Arctic curves of the four-vertex model ⋮ Limit shapes from harmonicity: dominos and the five vertex model ⋮ The genus-zero five-vertex model ⋮ Second class particles and limit shapes of evacuation and sliding paths for random tableaux.

Cites Work

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• Arctic curves of the six-vertex model on generic domains: the tangent method
• Minimizers of convex functionals arising in random surfaces
• The shape of a typical boxed plane partition
• Arctic curve of the free-fermion six-vertex model in an L-shaped domain
• Local statistics for random domino tilings of the Aztec diamond
• Limit shapes for the asymmetric five vertex model
• Limit shapes and the complex Burgers equation
• Dimers and amoebae
• A variational principle for domino tilings
• Fixed-energy harmonic functions

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