Zeitschrift für Analysis und ihre Anwendungen


Full-Text PDF (1210 KB) | Metadata | Table of Contents | ZAA summary
Volume 15, Issue 3, 1996, pp. 687–707
DOI: 10.4171/ZAA/723

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

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

(1) Depto. de Matematica Aplicada, Universidad de Cantabria, 39071, Santandér, Spain
(2) Institut für Mathematik, Technische Universität Berlin, Strasse des 17. Juni 136, 10623, Berlin, Germany
(3) Fakultät für Mathematik, Technische Universität Chemnitz, Reichenhainer Strasse 41, 09107, 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