Abstract

We consider functionals of the calculus of variations subjected to constraints of the form ∫Ωg(x,u) dx=1\int_\Omega g(x, u)\, dx = 1. We identify the relaxed problem and we show that, when a lack of compactness occurs, the constraint may relax to a gap term.

Author information

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Giuseppe Buttazzo

Dipartimento di Matematica, Università di Pisa, Via Buonarroti 2, 56127 Pisa, Italy.

Victor J. Mizel

Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA 15213, USA.

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Suggested citation

G. Buttazzo, V. J. Mizel. “On a Gap Phenomenon for Isoperimetrically Constrained Variational Problems.” Journal of Convex Analysis 2 (1995), No. 1&2, 87–101. https://doi.org/10.68381/jca02006

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Published by Heldermann Verlag, 1995. Rights now held by Banach Press LLC.