On Problems in the Calculus of Variations in Increasingly Elongated Domains

Abstract

This paper deals with minimization problems in the calculus of variations set in a sequence of domains, the size of which tends to infinity in certain directions and such that the data only depend on the coordinates in the directions that remain constant. The authors study the asymptotic behavior of minimizers in various situations and show that they converge in an appropriate sense toward minimizers of a related energy functional in the constant directions.

Keywords

Calculus of variations / Domains becoming unbounded / Asymptotic behavior / Exponential rate of convergence

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