An Application of the Browder-Minty Theorem in a Problem of Partial Differential Equations
DOI:
https://doi.org/10.35819/remat2020v6i1id3524Keywords:
Elliptic Problems, Browder-Minty Theorem, Weak Solution, Functional AnalysisAbstract
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.
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How to Cite
https://orcid.org/0000-0002-0893-7426
