scholarly journals Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

2015 ◽  
Vol 37 (4) ◽  
pp. A1637-A1657 ◽  
Author(s):  
Mario Amrein ◽  
Thomas P. Wihler
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Elliptic Partial Differential Equations ◽  
Galerkin Methods ◽  
Partial Differential ◽  
Semilinear Elliptic ◽  
Fully Adaptive

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

2019 ◽  
Vol 6 (1) ◽  
pp. 1-12
Author(s):  
Westher Manricky Bernardes Fortunato ◽  
Dassael Fabricio dos Reis Santos
Keyword(s):  
Weak Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Main Tool ◽  
Elliptic Partial Differential Equations ◽  
Hölder Inequality ◽  
Partial Differential ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Continuous Operators

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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