Conference Description:

The scope of this meeting is to gather researchers interested in the study of elliptic and parabolic equations via the Maximum Principle.

This conference will be in spirit a sequel to the conferences Positivity: a key to fully - nonlinear equations (Vietri 2010), Mostly Maximum Principle (Roma 2012, Agropoli 2015 and Banff 2017). This edition will be held at the Palazzone (Cortona, Italy).
This series has started as a relatively small gathering of high level mathematicians working in areas related with the maximum principle, and has expanded in themes and number of participants, but without diminishing the level of the mathematicians involved and without losing the original spirit.

The maximum principle arises in so many instances and problems that we cannot hope to cover them all. During the Conference, we will mainly focus on the following aspects:
- Comparison principle and spectral properties
- Hamilton-Jacobi equations
- Liouville type results
- Minimal surfaces
- Parabolic equations: asymptotic analysis, traveling fronts
- Qualitative properties such as symmetry, lack of symmetry, overdetermined problems
- Regularity of solutions for fully nonlinear operators be they elliptic, degenerate elliptic, local or non local