Sobre a Teoria de Regularidade Elíptica via Análise da Equação de Helmholtz em RN
Elliptic Partial Differential Equations; Helmholtz Equation; Variational Methods; Modified Bessel Functions; Agmon-Douglis-Nirenberg Theorem.
In this work we demonstrate an important regularity result for the Helmholtz problem in unbounded domains and, furthermore, we show that this result can be used to regularize even weak solutions of semi-linear elliptic problems in RN. To achieve our goals, it will be of vital importance the use of Bessel’s Modified Function Theory, Calderón-Zygmund Theory, the Mountain Pass Theorem and Schauder’s Theorem, as well as basic results of Measure and Integration, Complex Analysis, Functional Analysis and the Theory of Sobolev Spaces.