Please use this identifier to cite or link to this item:
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
Source: 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
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.
Type: Article
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 PDFThumbnail
Show full item record

CORE Recommender

Page view(s) 20

checked on Jun 15, 2021

Download(s) 20

checked on Jun 15, 2021

Google ScholarTM


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