Liouville's formulae and Hadamard variation with respect to general domain perturbations

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.

This paper will appear in Journal of Mathematical Society of Japan