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.

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.