Second order directional shape derivatives

Titelangaben

Schiela, Anton ; Ortiz, Julian:
Second order directional shape derivatives.
Bayreuth , 2017 . - 29 S.

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Abstract

We propose a variant in the definition of a second order shape derivative. The result is a quadratic form in terms of one perturbation vector field that yields a second order quadratic model of the perturbed functional. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework, and give a detailed geometric interpretation of the arising terms.