Higher Hölder regularity for fractional ( p , q )-Laplace equations

We study the fractional ( p , q ) {(p,q)} -Laplace equation ( - Δ p ) s ⁢ u + ( - Δ q ) t ⁢ u = 0 see text (-Δₚ)ˢu+(-Δq)ᵗu=0 for s , t ∈ ( 0 , 1 ) {s,t∈(0,1)} and p , q ∈ ( 1 , ∞ ) {p,q∈(1,∞)} . We establish Hölder estimates with an explicit exponent. As a consequence, we derive a Liouville-type theorem. Our approach builds on techniques previously developed for the fractional p -Laplace equation, relying on a Moser-type iteration for difference quotients.