The gradient theory of phase transitions for systems with two potential wells
- 1 January 1989
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Royal Society of Edinburgh: Section A Mathematics
- Vol. 111 (1-2) , 89-102
- https://doi.org/10.1017/s030821050002504x
Abstract
Synopsis: In this paper we generalise the gradient theory of phase transitions to the vector valued case. We consider the family of perturbations of the nonconvex functional where W:RN→R supports two phases and N ≧1. We obtain the Γ(L1(Ω))-limit of the sequence Moreover, we improve a compactness result ensuring the existence of a subsequence of minimisers of Eε(·) converging in L1(Ω) to a minimiser of E0(·) with minimal interfacial area.This publication has 10 references indexed in Scilit:
- Local minimisers and singular perturbationsProceedings of the Royal Society of Edinburgh: Section A Mathematics, 1989
- The effect of a singular perturbation on nonconvex variational problemsArchive for Rational Mechanics and Analysis, 1988
- The gradient theory of phase transitions and the minimal interface criterionArchive for Rational Mechanics and Analysis, 1987
- Some Results and Conjectures in the Gradient Theory of Phase TransitionsPublished by Springer Nature ,1987
- Existence and stability of necking deformations for nonlinearly elastic rodsArchive for Rational Mechanics and Analysis, 1987
- On phase transitions with bulk, interfacial, and boundary EnergyArchive for Rational Mechanics and Analysis, 1986
- Asymptotic location of nodal lines using geodesic theoryThe Journal of the Australian Mathematical Society. Series B. Applied Mathematics, 1986
- On a theory of phase transitions with interfacial energyArchive for Rational Mechanics and Analysis, 1985
- Minimal Surfaces and Functions of Bounded VariationPublished by Springer Nature ,1984
- Structured phase transitions on a finite intervalArchive for Rational Mechanics and Analysis, 1984