Weighted decay estimates for the wave equation

Piero D'Ancona, Vladimir Georgiev, Hideo Kubo

研究成果: Article査読

35 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)1/2xj, j = 1, ..., 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 by V. Georgiev (1997, Amer. J. Math. 119, 1291-1319) and establish global existence results 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)146-208
ページ数63
ジャーナルJournal of Differential Equations
177
1
DOI
出版ステータスPublished - 2001 11 20
外部発表はい

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

フィンガープリント 「Weighted decay estimates for the wave equation」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル