In this work we study weighted Sobolev spaces in R-n generated by the Lie algebra of vector fields (1 + x(2))(1/2)partial derivative(xj), j = 1,..,n. Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in R-n. 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. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.
Weighted Strichartz estimate for the wave equation / D'Ancona, Piero Antonio; Vladimir, Georgiev; Hideo, Kubo. - In: COMPTES RENDUS DE L'ACADÉMIE DES SCIENCES. SÉRIE 1, MATHÉMATIQUE. - ISSN 0764-4442. - 330:5(2000), pp. 349-354. [10.1016/s0764-4442(00)00161-0]
Weighted Strichartz estimate for the wave equation
D'ANCONA, Piero Antonio;
2000
Abstract
In this work we study weighted Sobolev spaces in R-n generated by the Lie algebra of vector fields (1 + x(2))(1/2)partial derivative(xj), j = 1,..,n. Interpolation properties and Sobolev embeddings are obtained on the basis of a suitable localization in R-n. 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. (C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
