Cálculo funcional associado a problemas com condições dinâmicas de contorno

Abstract

This work aims to study the holomorphic functional calculus associated with a problem with dynamic boundary conditions defined on $\Omega$, where $\Omega \subset \mathbb{R}^n$ is a bounded and connected open set with $C^\infty$ boundary $\Gamma = \partial \Omega$. Our main goal is to show that the sectorial operator associated with this problem has a bounded $H_\infty$ functional calculus and, for this purpose, we will utilize tools from the Boutet de Monvel calculus, as well as concepts from Functional Analysis.