Weighted Strichartz estimate for the wave equation and low regularity solutions

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

研究成果: Article査読

1 被引用数 (Scopus)

抄録

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.

本文言語English
ページ(範囲)51-61
ページ数11
ジャーナルRendiconti dell'Istituto di Matematica dell'Universita di Trieste
31
出版ステータスPublished - 2000 1 1
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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