Chaitan P. Gupta, Ying C. Kwong, "Biharmonic eigen-value problems and estimates", International Journal of Mathematics and Mathematical Sciences, vol. 13, Article ID 575162, 12 pages, 1990. https://doi.org/10.1155/S0161171290000692
Biharmonic eigen-value problems and estimates
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 -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.
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.