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Zeitschrift für Analysis und ihre Anwendungen


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Volume 10, Issue 4, 1991, pp. 535–540
DOI: 10.4171/ZAA/474

Published online: 1991-12-31

Über eine Veraligemeinerung der Legendre-Hadamardschen Bedingung auf restringierte Variationsprobleme

Rolf Klötzler[1]

(1) Borsdorf, Germany

Variational problems are studied with continuous integrand, subject to vector-valued functions $x$ of vector variables $t$ with restricted derivatives $x_t$ under some goodness conditions of their feasible set $X$. For an optimal solution $x_o$ it will be shown the necessity of the (strong) quasi-convexity (in the sense of C. B. Morrey) of the integrand on $X$ in regard of $x_o$.

Keywords: Legendre-Hadamardsche Bedingung, $q$-Konvexität

Klötzler Rolf: Über eine Veraligemeinerung der Legendre-Hadamardschen Bedingung auf restringierte Variationsprobleme. Z. Anal. Anwend. 10 (1991), 535-540. doi: 10.4171/ZAA/474