Special Session 66: Geometric insights in Partial Differential Equations: advances and challenges

Regularity for (s,p)-harmonic functions
Verena Bogelein
University of Salzburg
Austria
Co-Author(s):    Frank Duzaar, Naian Liao, Giovanni Molica Bisci, and Raffaella Servadei
Abstract:
We report on higher Sobolev and H\"older regularity results for local weak solutions of the fractional $p$-Laplace equation of order $s\in(0,1)$ with $1\lt p\lt \infty$. The relevant estimates are stable when the fractional order $s$ reaches 1, and the known Sobolev regularity estimates for weak solutions of the local $p$-Laplace equation are recovered. The talk is based on joint work with Frank Duzaar (Salzburg), Naian Liao (Salzburg), Giovanni Molica Bisci (Urbino), and Raffaella Servadei (Urbino).