Affiliation:
1. Tata Institute of Fundamental Research , Centre for Applicable Mathematics , Bangalore , Karnataka, 560065 , India
Abstract
Abstract
We prove local Lipschitz regularity for bounded minimizers of functionals with nonstandard
(
p
,
q
)
{(p,q)}
-growth with the source term in the Lorentz space
L
(
N
,
1
)
{L(N,1)}
under the restriction
q
<
p
+
1
+
p
min
{
1
N
,
2
(
p
-
1
)
N
p
-
2
p
+
2
}
.
q<p+1+p\min\Bigl{\{}\frac{1}{N},\frac{2(p-1)}{Np-2p+2}\Bigr{\}}.
This extends the recent work by Beck and Mingione to bounded minimizers under weaker hypothesis and is sharp for some special ranges of p, q and N.
Subject
Applied Mathematics,General Mathematics
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p
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q
)
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(
p
,
q
)
(p,q)
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Cited by
2 articles.
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