Shape optimization for semi-linear elliptic equations based on an embedding domain method

Shape optimization for semi-linear elliptic equations based on an embedding domain method We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ 2 . A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Applied Mathematics and Optimization Springer Journals

Shape optimization for semi-linear elliptic equations based on an embedding domain method

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Copyright © 2004 by Springer-Verlag
Mathematics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization; Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Methods
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