Cours fondamental 2 (EDP,HFE,Phy)
Elliptic equations and regularity estimates
Helge Dietert
Contact : helge.dietert à imj-prg.fr
Des notes de cours seront disponibles.
Présentation
Elliptic equations appear in many areas of PDEs ranging from applied problems to differential geometry. Moreover, the developed techniques are fundamental for further applications. Here we will introduce regularity estimates and outlook their applications.
Contenu
- Review on PDEs: weak formulation of solutions
- First regularity estimates for solutions: Schauder estimates and Calderon-Zygmund theory
- Regularity for rough coefficients, De Giorgi-Nash-Moser theory and Hilbert's 19th problem
- Outlook: degenerate equations (Lewy's counterexample, H{\"o}rmander's hypoellipticity) and the Bernstein problem in differential geometry
Prérequis
Basic notions of Sobolev spaces
Bibliographie