Some Phragmén-Lindelöf type results for the biharmonic equation
type: Item
instance of: scholarly article
title: Some Phragmén-Lindelöf type results for the biharmonic equation
zbMATH Open document ID: 0810.31001
DOI: 10.1007/BF00945929
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1994-10-05T00:00:00Z
review text: Eliminating a priori decay assumptions of Phragmén-Lindelöf type, growth-decay estimates for some weighted and unweighted energy expressions are derived. Three special types of unbounded domains (so- called semi-infinite strips of variable thickness) in \(\mathbb{R}^ 2\) with Dirichlet type boundary conditions are considered. The derivations are based on the application of the Wirtinger and Schwarz inequalities. The basic inequality which is used to prove the energy estimates is \[ |\varphi (z)|\leq (h^ 2/2\pi) \varphi''(z). \] Explicit bounds are also given for the total energy. The end of the paper outlines how the obtained results for 2D may be extended to analogous problems in \(\mathbb{R}^ 3\).
Mathematics Subject Classification ID: 31A30
Mathematics Subject Classification ID: 35J35
Mathematics Subject Classification ID: 35Q72
zbMATH DE Number: 636031
zbMATH Keywords: biharmonic equation
zbMATH Keywords: energy estimation
zbMATH Keywords: semi infinite strips
zbMATH Keywords: decay
author: L. E. Payne
author: Philip Schaefer
reviewed by: István Ecsedi
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00945929
OpenAlex ID: W2003883403
description: scientific article; zbMATH DE number 636031