Abstract
In this paper we obtain the following weighted
L
p
-type regularity estimates
B
(
|
f
|
)
∈
L
q
(
ν
,
ν
+
T
;
L
w
q
(
Ω
)
)
locally
⇒
B
(
|
∇
u
|
)
∈
L
q
(
ν
,
ν
+
T
;
L
w
q
(
Ω
)
)
locally
for any
q
>
1
of weak solutions for non-homogeneous nonlinear parabolic equations with Orlicz growth
u
t
−
div
(
a
(
(
A
∇
u
⋅
∇
u
)
1
2
)
A
∇
u
)
=
div
(
a
(
|
f
|
)
f
)
under some proper assumptions on the functions
a
,
w
,
A
and
f
, where
B
(
t
)
=
∫
0
t
τ
a
(
τ
)
d
τ
. Moreover, we remark that two natural examples of functions
a
(
t
)
are
a
(
t
)
=
t
p
−
2
(
p
-Laplace equation)
and
a
(
t
)
=
t
p
−
2
log
α
(
1
+
t
)
for
α
>
0.
Moreover, our results improve the known results for such equations.