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 language | French |
|---|---|
| Pages (from-to) | 349-354 |
| Number of pages | 6 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 330 |
| Issue number | 5 |
| Publication status | Published - 2000 Mar 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Mathematics(all)
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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 journal › Article
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TY - JOUR
T1 - Une estimation de Strichartz avec poids pour l'équation des ondes
AU - D'Ancona, Piero
AU - Gueorguiev, Vladimir Simeonov
AU - Kubo, Hideo
PY - 2000/3/1
Y1 - 2000/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0034147290&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0034147290&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0034147290
VL - 330
SP - 349
EP - 354
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 5
ER -