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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Nonconvex variational problems with general singular perturbations

Author: Nicholas C. Owen
Journal: Trans. Amer. Math. Soc. 310 (1988), 393-404
MSC: Primary 49A50; Secondary 49F10, 58E15, 73C60, 73K05
MathSciNet review: 965760
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Abstract: We study the effect of a general singular perturbation on a nonconvex variational problem with infinitely many solutions. Using a scaling argument and the theory of $ \Gamma $-convergence of nonlinear functionals, we show that if the solutions of the perturbed problem converge in $ {L^1}$ as the perturbation parameter goes to zero, then the limit function satisfies a classical minimal surface problem.

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Article copyright: © Copyright 1988 American Mathematical Society