Galerkin approximation, strong continuity of the relative rearrangement map and application to plasma physics equations
type: Item
instance of: scholarly article
title: Galerkin approximation, strong continuity of the relative rearrangement map and application to plasma physics equations
zbMATH Open document ID: 1005.76097
published in: Differential and Integral Equations
publication date: 2003-01-26T00:00:00Z
review text: The Galerkin method is applied to solve the nonlinear equation \(\Delta u = F(u)\) in an open bounded connected set of \(\mathbb{R}^N\), \(N\geq 2\). Based on the Brouwer fixed-point theorem, Sobolev space techniques and eigenfunctions of Laplace operator with Dirichlet boundary conditions, the author proves the unique solvability of this problem. The theory is applied to plasma physics equations.
reviewed by: Michal Křížek
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 35Q60
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1858736
zbMATH Keywords: nonlinear elliptic equations
zbMATH Keywords: Laplace operator
zbMATH Keywords: Galerkin method
zbMATH Keywords: strong continuity
zbMATH Keywords: eigenvalues
zbMATH Keywords: eigenfunctions
zbMATH Keywords: relative rearrangement map
zbMATH Keywords: Brouwer fixed-point theorem
zbMATH Keywords: Sobolev space
zbMATH Keywords: Dirichlet boundary conditions
zbMATH Keywords: plasma physics
author: J.-M. Rakotoson
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1858736