Seminario di analisi matematica
ore
15:15
presso Aula Seminario VIII piano
In this talk we discuss some extensions of the classical Krylov-Safonov Harnack inequality. After reviewing the standard regularity theory, we will introduce a weaker notion of viscosity solutions.
The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior.
Roughly, our viscosity solutions satisfy comparison in a neighborhood of a touching point whose size depends on the properties of the test functions.
As an application, we recover the C^{1,\alpha} estimates of Almgren and Tamanini for quasi-minimizers of the perimeter functional.
We also establish the regularity of the free boundary for almost minimizers of one-phase type problems.