Weighted Strichartz estimate for the wave equation and low regularity solutions

P. D'ancona, Vladimir Simeonov Gueorguiev, H. Kubo

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

In this work we study weighted Sobolev spaces in Rn generated by the Lie algebra of vector fields (1 + |x|2)1/2 ∂xi, j = l,n...n. Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in Rn. As an application we derive weighted Lq estimates for the solution of the homogeneous wave equation. For the inhomogeneous wave equation we generalize the weighted Strichartz estimate established in [5] and estab lish global existence result for the supercritical semilinear wave equation with non compact small initial data in these weighted Sobolev spaces.

Original languageEnglish
Pages (from-to)51-61
Number of pages11
JournalRendiconti dell'Istituto di Matematica dell'Universita di Trieste
Volume31
Publication statusPublished - 2000 Jan 1
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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