Elliptic Regularity via Analysis of the Helmholtz Equation in RN
Elliptic Partial Differential Equations; Helmholtz Equation; Variational Methods; Modified Bessel Functions; Agmon-Douglis-Nirenberg Theorem;
In this work we present an important regularity result for the Helmholtz Equation in unbounded domains due to C. A. Stuart and, furthermore, we show that this result can also be used to regularize weak solutions of nonlinear elliptic problems in RN. In order 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.