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On the Convergence of a Class of Nonlocal Elliptic Equations and Related Optimal Design Problems

  • Fuensanta Andrés
  • Julio Muñoz
Article

Abstract

A convergence result for a nonlocal differential equation problem is proved. As a by-product, some results about the convergence for a type of nonlocal optimal design are given. Since these problems give rise to local design problems in the limit, different results on classical existence are obtained as well. Concerning the nonlocal formulation, the state equation is of nonlocal elliptic type and the cost functional we analyze includes, among other cases, an approximation of the square of the gradient.

Keywords

Approximation of partial differential equations Optimal control Integral equations G-convergence 

Mathematics Subject Classification

35J20 49J22 45A05 46N20 

Notes

Acknowledgments

We are profoundly grateful to P. Pedregal for his encouragement and helpful comments. We also want to thank J. C. Bellido for interesting discussions on the subject.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Universidad de Castilla-La ManchaToledoSpain

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