tailieunhanh - Báo cáo hóa học: " Research Article Degenerate Anisotropic Differential Operators and Applications"

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Degenerate Anisotropic Differential Operators and Applications | Hindawi Publishing Corporation Boundary Value Problems Volume 2011 Article ID 268032 27 pages doi 2011 268032 Research Article Degenerate Anisotropic Differential Operators and Applications Ravi Agarwal 1 Donal O Regan 2 and Veli Shakhmurov3 1 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA 2 Department of Mathematics National University of Ireland Galway Ireland 3 Department of Electronics Engineering and Communication Okan University Akfirat Tuzla 34959 Istanbul Turkey Correspondence should be addressed to Veli Shakhmurov Received 2 December 2010 Accepted 18 January 2011 Academic Editor Gary Lieberman Copyright 2011 Ravi Agarwal et al. 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. The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued Lp spaces are given. Sharp estimates for resolvent discreetness of spectrum and completeness of root elements of the corresponding differential operators are obtained. In the last section some applications of the main results are given. 1. Introduction and Notations It is well known that many classes of PDEs pseudo-Des and integro-DEs can be expressed as differential-operator equations DOEs . As a result many authors investigated PDEs as a result of single DOEs. DOEs in H-valued Hilbert space valued function spaces have been studied extensively in the literature see 1-14 and the references therein . Maximal regularity properties for higher-order degenerate anisotropic DOEs with constant coefficients and nondegenerate equations with variable coefficients were studied in 15 16 . The main aim of the present paper is to discuss the separability properties