Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions

Details Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions Concerning the Strauss conjecture and almost global existence for nonlinear Dirichlet-wave equations in 4-dimensions

2007-10-10

arxiv.org/abs/0710.2026v2

Mathematics

Analysis of PDEs

Corrected a few typos and clarified the proof of inequality (2.12). 18 pages

Scientific paper

We show the obstacle version of the Strauss conjecture holds when the spatial
dimension is equal to 4. We also show that an almost global existence theorem
of H\"ormander for (4+1)-dimensional Minkowski space holds in the obstacle
setting. We use weighed space-time variants of the energy inequality and a
variant of the classical Hardy inequality.

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