Sobre a teoria de regularidade elíptica via análise da equação de Helmholtz em RN
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.
Equações diferenciais parciais elípticas, Equação de Helmholtz, Métodos variacionais, Funções modificadas de Bessel, Teorema de Agmon-Douglis-Nirenberg
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Universidade Federal do Rio Grande do Norte