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

• Main Authors: Westher Manricky Bernardes Fortunato, Dassael Fabricio dos Reis Santos
• Format: Article
• Language: Portuguese
• Published: Instituto Federal de Educação, Ciência e Tecnologia do Rio Grande do Sul (IFRS) 2019-12-01
• Series: REMAT
• Subjects: Elliptic Problems; Browder-Minty Theorem; Weak Solution; Functional Analysis
• Online Access: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/3524

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.