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Harnack inequality for harmonic functions relative to a nonlinear p -homogeneous Riemannian Dirichlet form
We consider a Riemannian ( p-homogeneous) Dirichlet functional Φ ( u ) = ∫ X μ ( u ) ( d x ) ( p > 1 ) defined on D, where D is a dense subspace of L p ( X , m ) and X is a locally compact Hausdorff topological space endowed with the distance d connected with Φ ( u ) (see Section 2 for the defini...
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| Published in: | Nonlinear analysis 2006, Vol.64 (1), p.51-68 |
|---|---|
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | We consider a Riemannian (
p-homogeneous) Dirichlet functional
Φ
(
u
)
=
∫
X
μ
(
u
)
(
d
x
)
(
p
>
1
)
defined on
D, where
D is a dense subspace of
L
p
(
X
,
m
)
and
X is a locally compact Hausdorff topological space endowed with the distance
d connected with
Φ
(
u
)
(see Section 2 for the definitions). We denote by
a
(
u
,
v
)
=
∫
X
μ
˜
(
u
,
v
)
(
d
x
)
the Dirichlet form related to
Φ
(
u
)
. We prove a Harnack type inequality for positive harmonic function relative to the form
a
(
u
,
v
)
; as a consequence we obtain also the Hölder continuity of harmonic function relative to the form
a
(
u
,
v
)
. |
|---|---|
| ISSN: | 0362-546X 1873-5215 |
| DOI: | 10.1016/j.na.2005.06.007 |