Analysis of multiplicity for a class of problems in calculus of variations

Abstract

This paper concerns the analysis of multiplicity for a class of problems of calculus of variations on manifolds, which include some problems arising in non-linear elasticity or in micromagnetism. For this class of problems, we develop an approach of geometrical and topological nature which enables the analysis of the structures of the sets of data admitting respectively one or several minimizers. In particular,we establish the Gs-denseness of the data admitting a unique minimizer and thenon-emptiness and the non-isolation of the set of data admitting several minimizers.We also give a geometrical characterization of the data entailing a loss of uniqueness.

Keywords:

• Calculus of variations on manifolds
• Multiplicity of minimizers
• Geometry in calculus of variations
• Leray-schauder degree

AMS:

• 49415
• 58B05
• 57N16

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Notes

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