Weak solutions of the cohomological equation on R² for regular vector fields

2014/01/21 by R. De Leo, Roberto De Leo, De Leo, Roberto
Mathematics · #Advanced Differential Equations and Dynamical Systems #Advanced Mathematical Physics Problems #Geometric Analysis and Curvature Flows #math.AP #math.DS

paper · pdf · doi:10.48550/arxiv.1401.5158

22 pages, 6 figures

arxiv created 2014/01/21 · arxiv updated 2014/01/22

Abstract

In a recent article, we studied the global solvability of the so-called cohomological equation L_X f=g in C^∞(\Rt), where X is a regular vector field on the plane and L_X the corresponding Lie derivative. In a joint article with T. Gramchev and A. Kirilov, we studied the existence of global L¹_loc weak solutions of the cohomological equation for vector fields depending only on one coordinate. Here we generalize the results of both articles by providing explicit conditions for the existence of global weak solutions to the cohomological equation when X is intrinsically Hamiltonian or of finite type.

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