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

Fuensanta Andrés () and Julio Muñoz ()
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Fuensanta Andrés: Universidad de Castilla-La Mancha
Julio Muñoz: Universidad de Castilla-La Mancha

Journal of Optimization Theory and Applications, 2017, vol. 172, issue 1, No 3, 33-55

Abstract: 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; 35J20; 49J22; 45A05; 46N20 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-016-1021-z

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