Nonhomogeneous biharmonic problem in the half-space, \(L^{p}\) theory and generalized solutions
type: Item
instance of: scholarly article
title: Nonhomogeneous biharmonic problem in the half-space, \(L^{p}\) theory and generalized solutions
zbMATH Open document ID: 1142.35015
author: Chérif Amrouche
author: Yves Raudin
published in: Journal of Differential Equations
publication date: 2007-05-11T00:00:00Z
review text: The aim of this pape is to solve of the biharmonic problem with nonhomogeneous boundary conditions \[ \Delta^2 u=f\quad\text{in }\mathbb{R}^N_+, \qquad u= g_0\quad\text{on }\Gamma= \mathbb{R}^{N-1}, \qquad \partial_N u= g_1\quad\text{on }\Gamma, \] where \(N\geq 2\). Using \(L^p\) theory, \(1< p<\infty\), the authors prove existence and uniqueness results, taking data from weighted Sobolev spaces. The analysis of the authors is based on the isomorphism properties of the biharmonic operator in the whole space and the solution of the Dirichlet and Neumann problems for the Laplacian in the half-space.
reviewed by: Messoud Efendiev
Mathematics Subject Classification ID: 35J40
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 35J35
zbMATH DE Number: 5151788
zbMATH Keywords: biharmonic problem
zbMATH Keywords: half-space
zbMATH Keywords: weighted Sobolev spaces
MaRDI profile type: Publication
full work available at URL: j.jde.2007.01.018
OpenAlex ID: W2005673151
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DOI: 10.1016/J.JDE.2007.01.018
description: scientific article; zbMATH DE number 5151788