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On the topological derivative in shape optimization. (English) Zbl 0940.49026
Author’s abstract: “The topological derivative for an arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can be used for solving shape optimization problems in structural mechanics”.

MSC:
49Q10 Optimization of shapes other than minimal surfaces
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J50 Variational methods for elliptic systems
35B37 PDE in connection with control problems (MSC2000)
74P15 Topological methods for optimization problems in solid mechanics
74K99 Thin bodies, structures
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