arXiv Analytics

Sign in

arXiv:0805.4733 [math.AP]AbstractReferencesReviewsResources

Strichartz estimates for the wave equation on manifolds with boundary

Matthew D. Blair, Hart F. Smith, Christopher D. Sogge

Published 2008-05-30, updated 2009-01-08Version 3

We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain global existence in the subcricital case, as well as global existence for the critical equation with small data. We also can use our Strichartz estimates to prove scattering results for the critical wave equation with Dirichlet boundary conditions in 3-dimensions.

Comments: 16 pages. Couple of typos corrected, to appear in Annales de l'Institut Henri Poincare
Categories: math.AP, math.CA
Subjects: 35L70
Related articles: Most relevant | Search more
arXiv:0711.0275 [math.AP] (Published 2007-11-02)
Global existence for energy critical waves in 3-d domains : Neumann boundary conditions
arXiv:1305.2137 [math.AP] (Published 2013-05-09)
On the torsion function with Robin or Dirichlet boundary conditions
arXiv:math/0607631 [math.AP] (Published 2006-07-25)
Global existence for energy critical waves in 3-D domains

Links

Toolbox