Issue |
ESAIM: COCV
Volume 22, Number 3, July-September 2016
|
|
---|---|---|
Page(s) | 862 - 871 | |
DOI | https://doi.org/10.1051/cocv/2015034 | |
Published online | 14 June 2016 |
Strict convexity and the regularity of solutions to variational problems∗
Dipartimento di Matematica e Applicazioni, Università degli Studi
di Milano-Bicocca, Via R. Cozzi
53, 20125
Milano,
Italy
arrigo.cellina@unimib.it
Received:
12
December
2014
We consider the problem of minimizing where Ω is a bounded open subset
of ℝN and L is a convex function that
grows quadratically outside the unit ball, while, when | ∇v | <
1, it behaves like |
∇v | p with
1
<p<
2. We show that, for each ω ⊂ ⊂ Ω, there exists a constant
H,
depending on ω but not on p, such that both
in
particular, for every i =
1,...N, we have
.
Mathematics Subject Classification: 49K10
Key words: Regularity of solutions / higher differentiability / strict convexity
© EDP Sciences, SMAI 2016
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