Regularity theory for partial differential equations

The existence and uniqueness of the solution to the most important partial differential equations is often proved in some “weak sense” by general theoretical theorems of functional analysis. The regularity theory aims at proving that the weak solutions are actually smooth enough to satisfy the partial differential equations exactly the way that it is posed. It involves a broad variety of isolated issues including the Sobolev and Morrey embeddings, the Schauder estimates, the Harnack estimates, the blow-up methods.
The research team studies several families of partial differential equations, including evolution equations modeling physical phenomena, Kolmogorov equations, kinetic equations, Hörmander operators, equations arising in variational problems, obstacle problems.

[Ultimo aggiornamento: 04/02/2021 07:32:26]