Explicit \(L^\infty\)-norm estimates via Morse index for the bi-harmonic and tri-harmonic semilinear problems
type: Item
instance of: scholarly article
title: Explicit \(L^\infty\)-norm estimates via Morse index for the bi-harmonic and tri-harmonic semilinear problems
zbMATH Open document ID: 1421.35160
author: Foued Mtiri
author: A. Harrabi
author: Dong Ye
published in: Manuscripta Mathematica
publication date: 2019-04-30T00:00:00Z
review text: The authors of this article derive explicit $L^p$ and $L^\infty$ estimates for solutions of some polyharmonic elliptic equations using the Morse index. Precisely, they consider $(-\Delta)^ku=f(x,u)$ in a bounded domain $\Omega\subset \mathbb{R}^N$ with $N>2k$ having a smooth boundary. The boundary conditions under considerations are either Dirichlet or Navier boundary conditions. Here, $f$ is a $C^1(\overline{\Omega}\times \mathbb{R})$ function.
reviewed by: Andreas Kleefeld
Mathematics Subject Classification ID: 35J91
Mathematics Subject Classification ID: 31B30
Mathematics Subject Classification ID: 35J40
zbMATH DE Number: 7049115
zbMATH Keywords: polyharmonic elliptic equations
zbMATH Keywords: Dirichlet boundary condition
zbMATH Keywords: Navier boundary condition
MaRDI profile type: Publication
full work available at URL: s00229-018-1037-9
OpenAlex ID: W2803659431
cites work: Solutions of superlinear elliptic equations and their morse indices
cites work: Infinite dimensional Morse theory and multiple solution problems
cites work: Morse indices of solutions for super-linear elliptic PDE's
cites work: A priori bounds and a Liouville theorem on a half-space for higher-order elliptic Dirichlet problems
cites work: Existence results and a priori bounds for higher order elliptic equations and systems
cites work: Q4315396
cites work: Q5485942
cites work: Nodal sets and Morse indices of solutions of super-linear elliptic PDEs
DOI: 10.1007/S00229-018-1037-9
description: scientific article; zbMATH DE number 7049115