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Second order directional shape derivatives of integrals on submanifolds

  • * Corresponding author: Anton Schiela

    * Corresponding author: Anton Schiela 
This work was supported by DFG grant SCHI 1379/3-1
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  • We compute first and second order shape sensitivities of integrals on smooth submanifolds using a variant of shape differentiation. 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.

    Mathematics Subject Classification: Primary: 53A07, 49Q10, 49Q12.

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