Special Session 70: Progress and Challenges in Nonlocal and Nonhomogeneous PDEs

Regularity results and maximum principles for quasilinear operators of mixed local-nonlocal type
Carlo Alberto Antonini
INdAM (National Institute of High Mathematics)
Italy
Co-Author(s):    
Abstract:
In this talk, we will deal with mixed local-nonlocal quasilinear operators, modeled upon the sum of a $p$-Laplacian and a fractional $(s,q)$-Laplace operator, i.e., $-\Delta_p u+(-\Delta_q)^s u$. We will review some recent results concerning local and global regularity of their solutions, and we will address the validity of maximum principles and Hopf Lemma for such operators. Based on a series of joint works with M. Cozzi and P. Baroni.