Local minimisers of a three-phase partition problem with triple junctions

DOI10.1017/S0308210500030110zbMath0843.49025MaRDI QIDQ4328031

William P. Ziemer, Peter Sternberg

Publication date: 11 August 1996

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

phase transitionlocal minimizersmotion by curvatureCahn-Hilliard evolutionGinzburg-Landau evolutionthree-phase partition problem

Mathematics Subject Classification ID

Thermodynamics in solid mechanics (74A15) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (11)

On the heteroclinic connection problem for multi-well gradient systems ⋮ Dimension Reduction for the Landau--de Gennes Model: The Vanishing Nematic Correlation Length Limit ⋮ On the structure of minimizers of the Allen-Cahn energy for \(Z_N\) symmetric nonnegative potentials with \(N+1\) zeros ⋮ On the existence of \(N\)-junctions for a symmetric nonnegative potential with \(N+1\) zeros ⋮ On the triple junction problem without symmetry hypotheses ⋮ Duality theorem for a three-phase partition problem ⋮ Hamiltonian identities for elliptic partial differential equations ⋮ NUMERICAL SOLUTIONS OF A VECTOR GINZBURG–LANDAU EQUATION WITH A TRIPLE-WELL POTENTIAL ⋮ Higher energy solutions in the theory of phase transitions: A variational approach ⋮ Stability of stationary interfaces of binary-tree type ⋮ A variational approach to three-phase traveling waves for a gradient system

Cites Work

• Unnamed Item
• Minimal interface criterion for phase transitions in mixtures of Cahn- Hilliard fluids
• The effect of a singular perturbation on nonconvex variational problems
• The gradient theory of phase transitions and the minimal interface criterion
• Fast Reaction, Slow Diffusion, and Curve Shortening
• The gradient theory of phase transitions for systems with two potential wells
• Local minimisers and singular perturbations
• Weakly Differentiable Functions

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