Über eine Veraligemeinerung der Legendre-Hadamardschen Bedingung auf restringierte Variationsprobleme

Abstract

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 $x_o$.