Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

Journal Article · Mon Mar 15 00:00:00 EST 2004 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-003-0787-1· OSTI ID:21067458

Slawig, Thomas ^[1]

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1. Institut fuer Mathematik MA 4-5, Technische Universitaet Berlin, 10623 Berlin (Germany)

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in R{sup 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.

• OSTI ID: 21067458
• Journal Information: Applied Mathematics and Optimization, Vol. 49, Issue 2; Other Information: DOI: 10.1007/s00245-003-0787-1; Copyright (c) 2004 Springer-Verlag; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BOUNDARY CONDITIONS
DIRICHLET PROBLEM
EQUATIONS
FUNCTIONS
LAPLACIAN
MATHEMATICAL SOLUTIONS
OPTIMIZATION