- 08-77 Massimiliano Berti, Philippe Bolle
- Sobolev periodic solutions of nonlinear wave equations in higher spatial dimensions.
Apr 14, 08
(auto. generated pdf),
of related papers
Abstract. We prove the existence of Cantor families of periodic solutions for nonlinear
wave equations in higher spatial dimensions with periodic boundary conditions.
We study both forced and autonomous PDEs. In the latter case, our theorems
generalize previous results of Bourgain to more general nonlinearities of
class $C^k$ and assuming weaker non-resonance conditions. Our solutions
have Sobolev regularity both in time and space. The proofs are based on
a differentiable Nash-Moser iteration scheme, where it is sufficient to get estimates
of interpolation type for the inverse linearized operators. Our approach
works also in the presence of very large "clusters of small divisors".