Abstract
The regularity of eigenvalues of elliptic operators upon deformations of a given bounded domain is a classical problem in elliptic PDEs which has been focused by many authors. We establish a theorem on Cr dependence of algebraically simple eigenvalues and eigenfunctions with respect to perturbations of C1 class of non-smooth domains and of Cr class of coefficients of elliptic operators. Moreover, we also compute the first variation of these eigenvalues in relation to both parameters for non-smooth domains. As a byproduct, we extend Hadamard's formula to second order elliptic operators for domains of C2 class and other non-smooth ones.
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