Weighted Strichartz estimate for the wave equation and low regularity solutions

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

研究成果: Article

1 引用 (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.

元の言語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
出版物ステータスPublished - 2000 1 1
外部発表Yes

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Strichartz Estimates
Weighted Estimates
Weighted Sobolev Spaces
Wave equation
Regularity
Sobolev Embedding
Semilinear Wave Equation
Global Existence
Existence Results
Vector Field
Lie Algebra
Interpolate
Generalise

ASJC Scopus subject areas

  • Mathematics(all)

これを引用

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