Global Solvability in Functional Spaces for Smooth Nonsingular Vector Fields in the Plane
Operator Theory Advances and Applications(2011)
摘要
We address some global solvability issues for classes of smooth nonsingular vector fields L in the plane related to cohomological equations Lu = f in geometry and dynamical systems. The first main result is that L is not surjective in C-infinity (R-2) if the geometrical condition the existence of separatrix strips holds. Next, for nonsurjective vector fields, we demonstrate that if the RHS f has at most infra-exponential growth in the separatrix strips we can find a global weak solution L-loc(1) near the boundaries of the separatrix strips. Finally we investigate the global solvability for perturbations with zero-order p.d.o. We provide examples showing that our estimates are sharp.
更多查看译文
关键词
Global solutions,separatrix strips,infra-exponential growth,pseudo-differential operators
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络