DOI: 10.1515/acv-2025-0119 ISSN: 1864-8258
Higher Hölder regularity for fractional (
p
,
q
)-Laplace equations
Prashanta Garain, Erik Lindgren Abstract
We study the fractional
(
p
,
q
)
{(p,q)}
-Laplace equation
(
-
Δ
p
)
s
u
+
(
-
Δ
q
)
t
u
=
0
see text
(-\Delta_{p})^{s}u+(-\Delta_{q})^{t}u=0
for
s
,
t
∈
(
0
,
1
)
{s,t\in(0,1)}
and
p
,
q
∈
(
1
,
∞
)
{p,q\in(1,\infty)}
. 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.