Optimal Potentials for Problems with Changing Sign Data

Giuseppe Buttazzo (), Faustino Maestre () and Bozhidar Velichkov ()
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Giuseppe Buttazzo: Università di Pisa
Faustino Maestre: Universidad de Sevilla
Bozhidar Velichkov: Université Grenoble Alpes

Journal of Optimization Theory and Applications, 2018, vol. 178, issue 3, No 4, 743-762

Abstract: Abstract In this paper, we consider variational optimal control problems. The state equation is an elliptic partial differential equation of a Schrödinger type, governed by the Laplace operator with a potential, with a right-hand side that may change sign. The control variable is the potential itself that may vary in a suitable admissible class of nonnegative potentials. The cost is an integral functional, linear (but non-monotone) with respect to the state function. We prove the existence of optimal potentials, and we provide some necessary conditions for optimality. Several numerical simulations are shown.

Keywords: Schrödinger operators; Optimal potentials; Shape optimization; Free boundary; Capacitary measures; Stochastic optimization; 49J45; 49Q10; 35J10; 49A22; 35J25; 49B60 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10957-018-1347-9

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