Affiliation:
1. Dipartimento di Matematica “Tullio Levi Civita” , Università di Padova , via Trieste 63, 35121 , Padova , Italy
Abstract
Abstract
We define a homogeneous De Giorgi class
of order
p
=
2
{p=2}
that contains the solutions of evolution equations of the types
ξ
(
x
,
t
)
u
t
+
A
u
=
0
{\xi(x,t)u_{t}+Au=0}
and
(
ξ
(
x
,
t
)
u
)
t
+
A
u
=
0
{(\xi(x,t)u)_{t}+Au=0}
,
where
ξ
>
0
{\xi>0}
almost everywhere and A is a suitable elliptic operator.
For functions belonging to this class, we prove a Harnack inequality.
As a byproduct, one can obtain Hölder continuity for solutions of a subclass of the first equation.
Subject
Applied Mathematics,Analysis
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