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
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
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.
Type: Article
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

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