Diferenciabilidade dos autovalores de operadores uniformemente elípticos de segunda ordem em domínios regulares e não-regulares

Abstract

In this work we present the differential calculus of domain, developed by Daniel Henry in 2005, applied to problems of boundary pertubation of the regular domain. We will use this technique to calculate the first derivative of the simple eigenvalue of Laplace operator with respect to the domain. Then we show the technique developed by Marcos Montenegro and Julian Haddad in 2015 to calculate the derivative of simple eigenvalues of uniformly elliptical operators of second order in non-regular domains, with respect to the coefficients of the operator and the domain, where they are taken Non-regular disturbances of the problem definition domain. Finally, we highlight some differences and similarities between both techniques.