Casas, Eduardo; Fernández, Luis Alberto Optimal control of quasilinear elliptic equations with non differentiable coefficients at the origin. (English) Zbl 0749.49006 Rev. Mat. Univ. Complutense Madr. 4, No. 2-3, 227-250 (1991). The authors study some optimal control problems involving the differential operator: \(Ay=-\text{div}(u(x,|\nabla y|)\nabla y)+v(x,y)\), with \(u: \Omega\times(0,\infty)\to(0,\infty)\) and \(v: \Omega\times R\to R\), where \(\Omega\) is a bounded open subset of \(R^ N\) with Lipschitz continuous boundary. In this paper, the non- differentiability of \(u(x,\cdot)\) at 0 is allowed, which causes the non- differentiability of state with respect to the control. The existence of a solution is proved. The optimality conditions are obtained by considering a perturbation of the coefficients of the differential operator \(A\). Reviewer: R.Stavre (Bucureşti) Cited in 13 Documents MSC: 49J20 Existence theories for optimal control problems involving partial differential equations 49K20 Optimality conditions for problems involving partial differential equations Keywords:quasilinear elliptic equation; non-differentiable coefficients; perturbed differential operator; differential operator; Lipschitz continuous boundary; non-differentiability PDFBibTeX XMLCite \textit{E. Casas} and \textit{L. A. Fernández}, Rev. Mat. Univ. Complutense Madr. 4, No. 2--3, 227--250 (1991; Zbl 0749.49006) Full Text: EuDML