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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Nonconvex variational problems with general singular perturbations
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by Nicholas C. Owen PDF
Trans. Amer. Math. Soc. 310 (1988), 393-404 Request permission

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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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 310 (1988), 393-404
  • MSC: Primary 49A50; Secondary 49F10, 58E15, 73C60, 73K05
  • DOI: https://doi.org/10.1090/S0002-9947-1988-0965760-9
  • MathSciNet review: 965760