This paper considers optimal control problems for systems governed by second order elliptic differential equations in divergence form with nonlinear terms and control appear in all terms. The representation of the main part of increment for a solution of the state equation is given in the case of needle-like variations.
Cite this article
Uldis Raitums, Necessary optimality conditions for systems described by nonlinear elliptic equations. I (in Russian). Z. Anal. Anwend. 3 (1984), no. 1, pp. 65–79DOI 10.4171/ZAA/90