Biharmonic eigen-value problems and Lp estimates

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.