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  4. Rendiconti dell’Istituto di Matematica dell’Università di Trieste: an International Journal of Mathematics
  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.31 (2000) s2
  6. Weighted Strichartz Estimate for the Wave Equation and Low Regularity Solutions
 
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Weighted Strichartz Estimate for the Wave Equation and Low Regularity Solutions

Georgiev, Vladimir
•
D'Ancona, P.
•
Kubo, Hideo
2000
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ISSN
0049-4704
http://hdl.handle.net/10077/4271
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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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
31 (2000) suppl.2
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.
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