Une estimation de Strichartz avec poids pour l'équation des ondes

Translated title of the contribution: Weighted Strichartz estimate for the wave equation *

Piero D'Ancona, Vladimir Simeonov Gueorguiev, Hideo Kubo

Research output: Contribution to journalArticle

2 Citations (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∂xj, 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 in [6] and establish global existence result for the supercritical semilinear wave equation with non-compact small initial data in these weighted Sobolev spaces.

Original languageFrench
Pages (from-to)349-354
Number of pages6
JournalComptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume330
Issue number5
Publication statusPublished - 2000 Mar 1
Externally publishedYes

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Une estimation de Strichartz avec poids pour l'équation des ondes. / D'Ancona, Piero; Gueorguiev, Vladimir Simeonov; Kubo, Hideo.

In: Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, Vol. 330, No. 5, 01.03.2000, p. 349-354.

Research output: Contribution to journalArticle

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