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.
Funding Statement
This work was promoted in Research Institute for Mathematical Sciences (RIMS) Joint Research Program during 2019–2021. (RIMS is an International Joint Usage/Research Center located in Kyoto University.) The first author was supported by JSPS Grant-in-Aid for Scientific Research 19H01799. The second author was supported by JSPS Grant-in-Aid for Scientific Research 21K03372.
Citation
Takashi SUZUKI. Takuya TSUCHIYA. "Liouville's formulae and Hadamard variation with respect to general domain perturbations." J. Math. Soc. Japan 75 (3) 983 - 1024, July, 2023. https://doi.org/10.2969/jmsj/88958895
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