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International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 469-480
http://dx.doi.org/10.1155/S0161171290000692

Biharmonic eigen-value problems and Lp estimates

Department of Mathematical Sciences, Northern Illinois University, DeKalb, IL 60115, USA

Received 21 March 1989; Revised 20 October 1989

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Biharmonic eigen-values arise in the study of static equilibrium of an elastic body which has been suitably secured at the boundary. This paper is concerned mainly with the existence of and Lp-estimates for the solutions of certain biharmonic boundary value problems which are related to the first eigen-values of the associated biharmonic operators. The methods used in this paper consist of the “a-priori” estimates due to Agmon-Douglas-Nirenberg and P. L. Lions along with the Fredholm theory for compact operators.