TY - JOUR
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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U2 - 10.1016/S0764-4442(00)00161-0
DO - 10.1016/S0764-4442(00)00161-0
M3 - Article
AN - SCOPUS:0034147290
SN - 0764-4442
VL - 330
SP - 349
EP - 354
JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
JF - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
IS - 5
ER -