An Application of the Browder-Minty Theorem in a Problem of Partial Differential Equations

• Autor(a) principal: Fortunato, Westher Manricky Bernardes
• Data de Publicação: 2019
• Outros Autores: Santos, Dassael Fabricio dos Reis
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Remat (Bento Gonçalves)
• Texto Completo: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3524
• topic: Elliptic Problems; Browder-Minty Theorem; Weak Solution; Functional Analysis; Elliptic Problems; Browder-Minty Theorem; Weak Solution; Functional Analysis; Elliptic Problems; Browder-Minty Theorem; Weak Solution; Functional Analysis

In this work, we will show existence of weak solution for a semilinear elliptic problem using as main tool the Browder-Minty Theorem. First, we will make a brief introduction about basic theory of the Sobolev Spaces to support our study and provide sufficient tools for the development of our work. Then we will take a quick approach on the Browder-Minty Theorem and use this result to show the existence of at least one weak solution to an elliptic Partial Differential Equations (PDE) problem whose nonlinearity, denoted by f, is a known function. For this, in addition to the already mentioned results, we will also use as study tools: Embedding Sobolev Theorems, Linear Continuous Operators Theory, Poincaré Inequality and Hölder Inequality.