MATJ5101 Recent progress in regularity theory (JSS28) (2 op)
Osaamistavoitteet
To have an idea of basic regularity problems and results about regularity theory for solutions quasilinear degenerate equations and minimizers of integral functionals in the Calculus of Variations, with special emphasis on those parts touching so called Nonlinear Calder贸-Zygmund theory and Nonlinear Potential Theory.
Suoritustavat
Obligatory attendance on lectures, and completing exercises.
厂颈蝉盲濒迟枚
In this series of lectures I will try to summarize a few recent progresses in the regularity theory of quasilinear, possibly degenerate equations, after giving a rapid overview of basic facts. Specifically, I will move from basic and by now classical De Giorgi-Nash-Moser theory and partial regularity problems for systems, to more recent topics of current interest such as Nonlinear Calder贸n-Zygmund Theory and potential estimates in Nonlinear Potential Theory.
Esitietovaatimukset
Basic measure theory and functional analysis. Sobolev spaces. Notion of distributional solution.