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Abstract
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We revisit the question of regularity for minimizers of scalar autonomous integral functionals with
so-called
-growth.
In particular, we establish Lipschitz regularity under the condition
for
,
improving a classical result due to Marcellini (J. Differential Equations 90:1 (1991),
1–30).
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Keywords
nonuniformly elliptic equations, local Lipschitz
continuity, $(p,q)$-growth, nonstandard growth conditions
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Mathematical Subject Classification 2010
Primary: 35B65
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Milestones
Received: 18 May 2019
Revised: 10 July 2019
Accepted: 6 September 2019
Published: 10 November 2020
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