Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures

DOI10.1007/s00205-017-1112-5zbMath1375.35538arXiv1411.4008OpenAlexW1916662089MaRDI QIDQ2014377

Panayotis Smyrnelis, Peter W. Bates, Giorgio Fusco

Publication date: 11 August 2017

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.4008

zbMATH Keywords

reflection groupexistence resultpositive homomorphismvector Allen-Cahn equationequivariant classical solutionparabolic Allen-Cahn equation

Mathematics Subject Classification ID

Crystalline structure (74E15) Maximum principles in context of PDEs (35B50) Variational methods for elliptic systems (35J50) PDEs in connection with mechanics of deformable solids (35Q74) Semilinear parabolic equations (35K58) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91)

Related Items (9)

Layered solutions to the vector Allen-Cahn equation in \(\mathbb{R}^2\). Minimizers and heteroclinic connections ⋮ Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system ⋮ Unnamed Item ⋮ On the structure of minimizers of the Allen-Cahn energy for \(Z_N\) symmetric nonnegative potentials with \(N+1\) zeros ⋮ Entire minimizers of Allen-Cahn systems with sub-quadratic potentials ⋮ On the existence of \(N\)-junctions for a symmetric nonnegative potential with \(N+1\) zeros ⋮ On some elementary properties of vector minimizers of the Allen-Cahn energy ⋮ Unnamed Item ⋮ On the growth of the energy of entire solutions to the vector Allen-Cahn equation

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