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Mountain Pass Solutions for a Double-Well Energy

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Abstract:

We establish the existence of a mountain pass solution for a variational integral involving a quasiconvex function with a double-well structure in the geometrically linear elasticity setting. We show that under small dead-load perturbations, the Neumann boundary value problem has at least three solutions, a global minimizer, a local minimizer and a mountain pass solution. We show that our variational integral satisfies a Weak Palais–Smale condition (WPS) hence the mountain pass lemma applies. © 2002 Elsevier Science (USA).

Keywords: Young measure.; linear elastic strains; minimizers; mountain pass point; quasiconvex relaxation; quasimonotone mapping; two well

Document Type: Research Article

Affiliations: School of Mathematical Sciences, University of Sussex, Brighton, BN1 9QH, United Kingdom

Publication date: July 1, 2002

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