Embeddings, Hardy operators and nonlinear problems

作     者：Edmunds, D. E. 

作者机构：Univ Sussex Dept Math Brighton BN1 9RF E Sussex England 

出 版 物：《REVISTA MATEMATICA COMPLUTENSE》 (孔普卢顿数学杂志)

年 卷 期：2010年第23卷第2期

页      面：267-319页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Embeddings Function spaces Hardy operators Entropy numbers s-numbers Compact linear operators p-Laplacian 

摘      要：We survey some of the recent developments involving embeddings between function spaces. Emphasis is placed on improvements of classical Sobolev inequalities, the reduction of embedding questions to problems involving Hardy operators, and quantitative estimates of compactness of embeddings that have applications to the spectral theory of operators. We also consider a nonlinear eigenvalue problem which leads to a series representation of compact linear operators acting between Banach spaces, under mild restrictions on the spaces, thus establishing a complete analogue of E. Schmidt s classical Hilbert space theorem for compact operators. Information about relevant embedding maps enables the Dirichlet problem for the p-Laplacian to be studied, and a brief discussion is given of the generalizations of the trigonometric functions that appear naturally in this connection.