Strichartz estimates for the wave equation on manifolds with boundary

By Matthew D. Blair, Hart F. Smith, Christopher D. Sogge. 2008

132 citations recorded by the source corpus.

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 subcritical 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.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/40c2b7db3b5c75b5fbb6ab1cdd4f0270442b93b4

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In Applied Mathematics

In Control and Systems Engineering

In Mathematical Physics

Citations in the corpus

Dispersion for the wave equation inside strictly convex domains I: the Friedlander model case (2012, unknown): “All other positive results ([3] and references therein) rely instead on reflecting the metric across the boundary and considering a boundary less manifold with a Lipschitz metric across an interface, and then using the machinery originally developed for low regularity metrics [16, 20] and spectral c”
Injections de Sobolev probabilistes et applications (2011, background): “Il est possible que les résultats de la section 5 puissent aussi être étendus à ce cadre, mais la plage des estimations de Strichartz valides dans ce cadre des problèmes aux limites étant plus restreinte (voir [11, 20, 6]), cela nécessiterait une analyse plus précise.”