Journal Menu
- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
International Journal of Differential Equations
Volume 2012 (2012), Article ID 129691, 7 pages
doi: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.
Linked References
- O. Guès, “Probleme mixte hyperbolique quasi-lineaire caracteristique,” Comm. Partial Differential Equations, vol. 15, no. 5, pp. 595–645, 1990. View at Publisher · View at Google Scholar
- A. Morando and P. Secchi, “Regularity of weakly well posed hyperbolic mixed problems with characteristic boundary,” Journal of Hyperbolic Differential Equations, vol. 8, no. 1, pp. 37–99, 2011. View at Publisher · View at Google Scholar · View at Scopus
- A. Morando, P. Secchi, and P. Trebeschi, “Regularity of solutions to characteristic initial-boundary value problems for symmetrizable systems,” Journal of Hyperbolic Differential Equations, vol. 6, no. 4, pp. 753–808, 2009. View at Publisher · View at Google Scholar · View at Scopus
- M. Ohno, Y. Shizuta, and T. Yanagisawa, “The initial-boundary value problem for linear symmetric hyperbolic systems with boundary characteristic of constant multiplicity,” Kyoto Journal of Mathematics, vol. 35, no. 2, pp. 143–210, 1995.
- P. Secchi, “The initial-boundary value problem for linear symmetric hyperbolic systems with characteristic boundary of constant multiplicity,” Differential Integral Equations, vol. 9, no. 4, pp. 671–700, 1996.
- P. Secchi, “Well-posedness of characteristic symmetric hyperbolic systems,” Archive for Rational Mechanics and Analysis, vol. 134, no. 2, pp. 155–197, 1996. View at Scopus
- M. Ohno and T. Shirota, “On the initial-boundary-value problem for the linearized equations of magnetohydrodynamics,” Archive for Rational Mechanics and Analysis, vol. 144, no. 3, pp. 259–299, 1998. View at Scopus
- M. Tsuji, “Regularity of solutions of hyperbolic mixed problems with characteristic boundary,” Proceedings of the Japan Academy, vol. 48, pp. 719–724, 1972. View at Publisher · View at Google Scholar
- P. Secchi, “Well-posedness for a mixed problem for the equations of ideal Magneto-Hydrodynamics,” Archiv der Mathematik, vol. 64, no. 3, pp. 237–245, 1995. View at Publisher · View at Google Scholar · View at Scopus
- P. Secchi, “An initial boundary value problem in ideal Magneto-Hydrodynamics,” Nonlinear Differential Equations and Applications, vol. 9, no. 4, pp. 441–458, 2002. View at Scopus
- P. Secchi and Y. Trakhinin, “Well-posedness of the linearized plasma-vacuum interface problem.,” Submitted.
- Y. Trakhinin, “The existence of current-vortex sheets in ideal compressible magnetohydrodynamics,” Archive for Rational Mechanics and Analysis, vol. 191, no. 2, pp. 245–310, 2009. View at Publisher · View at Google Scholar · View at Scopus
- T. Yanagisawa and A. Matsumura, “The fixed boundary value problems for the equations of ideal Magneto-Hydrodynamics with a perfectly conducting wall condition,” Communications in Mathematical Physics, vol. 136, no. 1, pp. 119–140, 1991. View at Publisher · View at Google Scholar · View at Scopus
- M. Ohno, Y. Shizuta, and T. Yanagisawa, “The trace theorem on anisotropic Sobolev spaces,” Tohoku Mathematical Journal, vol. 46, no. 3, pp. 393–401, 1994.
- P. Secchi, “Some properties of anisotropic Sobolev spaces,” Archiv der Mathematik, vol. 75, no. 3, pp. 207–216, 2000. View at Scopus
- S. Alinhac, “Existence d'ondes de raréfaction pour des systèmes quasi-linéaires hyperboliques multidimensionnels,” Communications in Partial Differential Equations, vol. 14, no. 2, pp. 173–230, 1989.
- J. Francheteau and G. Métivier, “Existence de chocs faibles pour des systèmes quasi-linéaires hyperboliques multidimen- sionnels,” in Astérisque, vol. 268, pp. 1–198, 2000.
- D. Coutand and S. Shkoller, “Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum,” Communications on Pure and Applied Mathematics, vol. 64, no. 3, pp. 328–366, 2011. View at Publisher · View at Google Scholar · View at Scopus
- G. H. Hardy and J. E. Littlewood, Inequalities. Cambridge Mathematical Library, Cambridge, UK, Cambridge University Press, 1988.