Regularity for the fractional p-Laplace equation

Higher Sobolev and H\"older regularity is studied for local weak solutions of the fractional p-Laplace equation of order s in the case p≥ 2. Depending on the regime considered, i.e. 0<s-2/p or -2/p<s<1, precise local estimates are proven. The relevant estimates are stable if the fractional order s reaches $1$; the known Sobolev regularity estimates for the local p-Laplace are recovered. The case $p=2$ reproduces the almost W1+s,2loc-regularity for the fractional Laplace equation of any order s∈(0,1).