Entire Solutions with Six-fold Junctions to Elliptic Gradient Systems with Triangle Symmetry

DOI10.1515/ans-2013-0102zbMath1277.35157OpenAlexW2511102340MaRDI QIDQ4920719

Giorgio Fusco, Peter W. Bates, Panayotis Smyrnelis

Publication date: 22 May 2013

Published in: Advanced Nonlinear Studies (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/ans-2013-0102

zbMATH Keywords

invariant regiontriple junctionequivariant system

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Second-order elliptic systems (35J47) Entire solutions to PDEs (35B08) Symmetries, invariants, etc. in context of PDEs (35B06)

Related Items (5)

On the heteroclinic connection problem for multi-well gradient systems ⋮ Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system ⋮ Unnamed Item ⋮ On some elementary properties of vector minimizers of the Allen-Cahn energy ⋮ Multiphase solutions to the vector Allen-Cahn equation: crystalline and other complex symmetric structures

Cites Work

• The principle of symmetric criticality
• Stationary layered solutions in \(\mathbb{R}^ 2\) for an Allen-Cahn system with multiple well potential
• Triple-junction motion for an Allen-Cahn/Cahn-Hilliard system
• A uniform estimate for positive solutions of semilinear elliptic equations
• Symmetric quadruple phase transitions
• Existence of a solution to a vector-valued Allen-Cahn equation with a three well potential

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