Liouville's formulae and Hadamard variation with respect to general domain perturbations
Analysis of PDEs
2024-03-01 v2
Abstract
We study Hadamard variations with respect to general domain perturbations, particularly for the Neumann boundary condition. They are derived from new Liouville's formulae concerning the transformation of volume and area integrals. Then, relations to several geometric quantities are discussed; differential forms and the second fundamental form on the boundary.
Keywords
Cite
@article{arxiv.2210.00693,
title = {Liouville's formulae and Hadamard variation with respect to general domain perturbations},
author = {Takashi Suzuki and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:2210.00693},
year = {2024}
}
Comments
This paper will appear in Journal of Mathematical Society of Japan