Weighted decay estimates for the wave equation

Piero D'Ancona, Vladimir Simeonov Gueorguiev, Hideo Kubo

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

In this work we study weighted Sobolev spaces in Rn generated by the Lie algebra of vector fields (1 + x 2)1/2xj, 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 by V. Georgiev (1997, Amer. J. Math. 119, 1291-1319) and establish global existence results for the supercritical semilinear wave equation with non-compact small initial data in these weighted Sobolev spaces.

Original languageEnglish
Pages (from-to)146-208
Number of pages63
JournalJournal of Differential Equations
Volume177
Issue number1
DOIs
Publication statusPublished - 2001 Nov 20
Externally publishedYes

Fingerprint

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

Keywords

  • Decay estimates
  • Global solution
  • Semilinear equation
  • Supercritical
  • Wave equation
  • Weighted sobolev spaces

ASJC Scopus subject areas

  • Analysis

Cite this

Weighted decay estimates for the wave equation. / D'Ancona, Piero; Gueorguiev, Vladimir Simeonov; Kubo, Hideo.

In: Journal of Differential Equations, Vol. 177, No. 1, 20.11.2001, p. 146-208.

Research output: Contribution to journalArticle

D'Ancona, Piero ; Gueorguiev, Vladimir Simeonov ; Kubo, Hideo. / Weighted decay estimates for the wave equation. In: Journal of Differential Equations. 2001 ; Vol. 177, No. 1. pp. 146-208.
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