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Zeitschrift für Analysis und ihre Anwendungen


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Volume 18, Issue 2, 1999, pp. 469–489
DOI: 10.4171/ZAA/893

Published online: 1999-06-30

Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations

K. Malanowksi[1] and Fredi Tröltzsch[2]

(1) Polish Academy of Sciences, Warsaw, Poland
(2) Technische Universität Berlin, Germany

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, sufficient condi-tions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the $L^\{infty}$-norm. It is shown that these conditions are also necessary, provided that the dependence of data on the parameter is sufficiently strong.

Keywords: Parametric optimal control, semilinear parabolic equations, Lipschitz stability, generalized equations

Malanowksi K., Tröltzsch Fredi: Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations. Z. Anal. Anwend. 18 (1999), 469-489. doi: 10.4171/ZAA/893