Higher integrability for variational integrals with non-standard growth
2021 ◽
Vol 60
(2)
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Keyword(s):
AbstractWe consider autonomous integral functionals of the form $$\begin{aligned} {\mathcal {F}}[u]:=\int _\varOmega f(D u)\,dx \quad \text{ where } u:\varOmega \rightarrow {\mathbb {R}}^N, N\ge 1, \end{aligned}$$ F [ u ] : = ∫ Ω f ( D u ) d x where u : Ω → R N , N ≥ 1 , where the convex integrand f satisfies controlled (p, q)-growth conditions. We establish higher gradient integrability and partial regularity for minimizers of $${\mathcal {F}}$$ F assuming $$\frac{q}{p}<1+\frac{2}{n-1}$$ q p < 1 + 2 n - 1 , $$n\ge 3$$ n ≥ 3 . This improves earlier results valid under the more restrictive assumption $$\frac{q}{p}<1+\frac{2}{n}$$ q p < 1 + 2 n .
2008 ◽
Vol 188
(3)
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pp. 467-496
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Keyword(s):
2010 ◽
Vol 166
(3)
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pp. 259-281
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Keyword(s):
2019 ◽
Vol 12
(1)
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pp. 85-110
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2010 ◽
Vol 166
(3)
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pp. 239-258
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Keyword(s):
2009 ◽
Vol 38
(3-4)
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pp. 417-439
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1998 ◽
Vol 3
(1-2)
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pp. 41-64
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2016 ◽
Vol 439
(2)
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pp. 481-513
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