OpenstarTs >
EUT-Periodici >
Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics >
Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2 >

Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4271

Title: Weighted Strichartz Estimate for the Wave Equation and Low Regularity Solutions
Authors: Georgiev, Vladimir
D'Ancona, P.
Kubo, Hideo
Issue Date: 2000
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Citation: P. D'Ancona, V. Georgiev and H. Kubo, "Weighted Strichartz estimate for the wave equation and low regularity solutions", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 31 (2000) suppl.2, pp. 51-61.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
Abstract: In this work we study weighted Sobolev spaces in $\mathbf{R}^{n}$ generated by the Lie algebra of vector fields \[ \left(1+\mid x\mid^{2}\right)^{1/2}\partial_{x_{j}},\; j=1,...,n. \] Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in $\mathbf{R}^{n}$. As an application we derive weighted L$^{q}$ estimates for the solution of the homogeneous wave equation. For the inhomogeneous wave equation we generalize the weighted Strichartz estimate established in $\left[5\right]$ and establish global existence result for the supercritical semilinear wave equation with non compact small initial data in these weighted Sobolev spaces.
URI: http://hdl.handle.net/10077/4271
ISSN: 0049-4704
Appears in Collections:Rendiconti dell‘ Istituto di matematica dell‘ Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2

Files in This Item:

File Description SizeFormat
GeorgievDanconaKubo.pdf207.04 kBAdobe PDFView/Open
View Statistics

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.