Shape optimization for semi-linear elliptic equations based on an embedding domain method
The author studies shape optimization problems for semilinear elliptic equations with homogeneous Dirichlet boundary conditions in two dimension. A part of the boundary of the domain is parametrized by a smooth function \(\gamma\) from \([0,1]\) into \textbf{R}. Using the method of fictitious domains the author proves the continuity of the solution to the state equation with respect to variations of the domain, i.e., with respect to \(\gamma\). Next the Fréchet differentiability of a quadratic cost functional with respect to variations of the domain is also studied.
scientific article; zbMATH DE number 2101891