JournalszaaVol. 18, No. 2pp. 469–489

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

  • K. Malanowksi

    Polish Academy of Sciences, Warsaw, Poland
  • Fredi Tröltzsch

    Technische Universität Berlin, Germany
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Abstract

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.

Cite this article

K. Malanowksi, Fredi Tröltzsch, Lipschitz Stability of Solutions to Parametric Optimal Control Problems for Parabolic Equations. Z. Anal. Anwend. 18 (1999), no. 2, pp. 469–489

DOI 10.4171/ZAA/893