Concerning the Strauss Conjecture and Almost Global Existence for Nonlinear Dirichlet-wave Equations in 4-dimensions
نویسندگان
چکیده
The purpose of this paper is to show that certain sharp existence theorems for small amplitude nonlinear wave equations in the Minkowski space setting extend to the case of nonlinear Dirichlet-wave equations outside of obstacles. Our main result is that the obstacle version of the Strauss conjecture holds when the spatial dimension is equal to 4. The corresponding result for 4-dimensional Minkowski space was first proved by one of us [24]. In this paper we shall also show that Hörmander’s [5] almost global existence theorem for quasilinear equations extends to nonlinear Dirichlet-wave equations.
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