A Survey of Some Topics in Theory of Partial Differential Equations and Functional Analy sis

A Survey of Some Topics in Theory of Partial Differential Equations and Functional Analy- sis Denise Huet Institut Elie Cartan de Nancy, BP 239, 54506 Vandoeuvre les Nancy Cedex, France Abstract: The different themes, presented here, in the alphabetical order, are closely related to re- cent publications on partial differential equations and functional analysis . Some entries appeared in [H 2007]. The new entries are: Aubry type sets, Bounded variations (functions of), Fokker-Planck model , Mathieu-Hill type equations, Scattering metric, Sobolev spaces on metric measure spaces, Ultraparabolic equations, Wavefront sets. MSC classification: 3502; 4602; 35A18; 35B25; 35B40; 35J10; 35K57; 35L30 Key-words: Partial differential equations; Reaction-diffusion equations; Schrodinger equations; Fokker- Planck model; Pseudodifferential operators; Attractors; Sobolev spaces; Singular perturbations; Asymp- totic expansions. The origin of this survey is the reading of recent papers on the different topics. The development of each entry is, of course, non exhaustive; complements will be found in references in the main text, which, for convenience, are summarized at the end of the survey. The aim of this document is to provide guidance to advanced students and young researchers. A ATTRACTOR 1– Global attractor for an autonomous evolution equation.

• area condition


• ??r ?


• elliptic perturbations


• dimensional compact


• hamilton-jacobi equations


• equal


• boundary


• aubry-mather theory


• theory can