A survey of topics in analysis and differential equations

Denise Huet (1)

1 EDP - Equations aux dérivées partielles

This survey (or essay) is the result of reflexions suggested by recent publications. The topics, which are dealt with, are related to linear or nonlinear evolution equations, of first or second order in the time-variable, linear and nonlinear elliptic equations, spectral properties, singular perturbations, formation of layers, and spaces of functions, in particular of BMO or Sobolev type. They are presented in the alphabetical order, so that the article can be used as dictionary. The aim of this document is to provide guidance for (young) researchers in mathematics and applied sciences, biology, chemistry, mechanics and physics.

Mots clés: Attractors; fractals; evolution equations and systems; elliptic equations; Schrödinger operator; spectral theory; singular perturbations; internal and boundary layers; spaces of functions

Domaines: Equations aux dérivées partielles [math.AP]

Denise Huet. A survey of topics in analysis and differential equations. International Journal of Pure and Applied Mathematics, 2010, 62 (1), pp.79-128. ⟨hal-00394244⟩