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International Journal of Differential Equations
Volume 2012 (2012), Article ID 129691, 7 pages
http://dx.doi.org/10.1155/2012/129691
Research Article

A Higher-Order Hardy-Type Inequality in Anisotropic Sobolev Spaces

Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti 9, 25133 Brescia, Italy

Received 17 May 2012; Accepted 7 August 2012

Academic Editor: Jian-Ping Sun

Copyright © 2012 Paolo Secchi. 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

We prove a higher-order inequality of Hardy type for functions in anisotropic Sobolev spaces that vanish at the boundary of the space domain. This is an important calculus tool for the study of initial-boundary-value problems of symmetric hyperbolic systems with characteristic boundary.