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Zeitschrift für Analysis und ihre Anwendungen


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Volume 15, Issue 3, 1996, pp. 687–707
DOI: 10.4171/ZAA/723

Published online: 1996-09-30

Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem

E. Casas[1], Fredi Tröltzsch[2] and A. Unger[3]

(1) Universidad de Cantabria, Santander, Spain
(2) Technische Universität Berlin, Germany
(3) Technische Universität Chemnitz, Germany

In this paper sufficient second order optimality conditions are established for opti-mal control problems governed by a linear elliptic equation with nonlinear boundary condition, where pointwise constraints on the control are given. The second order condition requires coercivity of the Lagrange function on a suitable subspace together with first order sufficient conditions on a certain set of strongly active points.

Keywords: Optimal control, semilinear elliptic equations, second order conditions, sufficient optimality conditions

Casas E., Tröltzsch Fredi, Unger A.: Second Order Sufficient Optimality Conditions for a Nonlinear Elliptic Boundary Control Problem. Z. Anal. Anwend. 15 (1996), 687-707. doi: 10.4171/ZAA/723