Abstract
The differentiability of a potential energy with respect to variable domains in a nonlinear problem is shown as the differentiability of a functional with respect to a parameter using convex analysis in Banach spaces, where the parameter stands for mappings from a reference domain. We apply the abstract result to the differentiability of the p-Laplacian with respect to domains. The results are demonstrated within the framework of weak solution in view of the applications to fracture problems.
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Ohtsuka, K., Kimura, M. Differentiability of potential energies with a parameter and shape sensitivity analysis for nonlinear case: the p-Poisson problem. Japan J. Indust. Appl. Math. 29, 23–35 (2012). https://doi.org/10.1007/s13160-011-0049-6
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DOI: https://doi.org/10.1007/s13160-011-0049-6