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

Piero D'Ancona; Vladimir Georgiev; Hideo Kubo

doi:10.1016/S0764-4442(00)00161-0

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 Georgiev, Hideo Kubo

Research output: Contribution to journal › Article › peer-review

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∂x_j, 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 L^q 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.

Translated title of the contribution	Weighted Strichartz estimate for the wave equation *
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
DOIs	https://doi.org/10.1016/S0764-4442(00)00161-0
Publication status	Published - 2000 Mar 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1016/S0764-4442(00)00161-0

Cite this

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title = "Une estimation de Strichartz avec poids pour l'{\'e}quation des ondes",

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.",

author = "Piero D'Ancona and Vladimir Georgiev and Hideo Kubo",

note = "Funding Information: * The first and second authors were partially supported by the Programma Nazionale M.U.R.S.T. “Problemi e Metodi nella Teoria delle Equazioni Iperboliche. The third author was partially supported by Grant-in-Aid for Science Research (No.09304012), Ministry of Education, Science and Culture, Japan.",

year = "2000",

month = mar,

day = "1",

doi = "10.1016/S0764-4442(00)00161-0",

language = "French",

volume = "330",

pages = "349--354",

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T1 - Une estimation de Strichartz avec poids pour l'équation des ondes

AU - D'Ancona, Piero

AU - Georgiev, Vladimir

AU - Kubo, Hideo

N1 - Funding Information: * The first and second authors were partially supported by the Programma Nazionale M.U.R.S.T. “Problemi e Metodi nella Teoria delle Equazioni Iperboliche. The third author was partially supported by Grant-in-Aid for Science Research (No.09304012), Ministry of Education, Science and Culture, Japan.

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.

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JO - Comptes Rendus Mathematique

JF - Comptes Rendus Mathematique

SN - 1631-073X

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ER -

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

Abstract

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