Existence and regularity properties of solutions to fractional nonlinear problems

Scientific-Disciplinary Group

01/MATH-03 - Mathematical Analysis, Probability And Mathematical Statistics

Description

The research project is aimed at candidates working on PDEs, free boundary problems, calculus of variations and geometric measure theory.In particular, it will focus on existence and regularity results for nonlocal and nonlinear problems exhibiting growth conditions similar to the ones of the fractional p-Laplacian.The aim of this project is twofold:on one side we are interested in studying existence and non-existence results of non-constant positive solutions for a nonlinear subcritical fractional equation with nonlocal Neumann boundary conditions; on the other hand we aim to study interior regularity properties of solutions.While the regularity theory for the linear case p=2 is well understood, the case of the fractional p-Laplacian isis significantly more challenging to treat and some questions are still open.

Job posting website

https://bandi.unibo.it/ricerca/incarichi-di-ricerca

Funding body

ALMA MATER STUDIORUM - UNIVERSITA' DI BOLOGNA - - DIPARTIMENTO DI MATEMATICA

How to apply

Other

Selection process