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, VladimirD'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 Mathematics31 (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 thebasis of a suitable localization in $\mathbf{R}^{n}$. As an applicationwe derive weighted L$^{q}$ estimates for the solution of the homogeneouswave equation. For the inhomogeneous wave equation we generalize theweighted Strichartz estimate established in $\left[5\right]$ andestablish global existence result for the supercritical semilinearwave equation with non compact small initial data in these weightedSobolev 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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