We consider the problem of minimizing {equation presented} where Ω is a bounded open subset of RN and L is a convex function that grows quadratically outside the unit ball, while, when |∇ν| < 1, it behaves like |∇ν|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 {equation presented} in particular, for every i = 1, ...N, we have max {equation presented}.
Cellina, A. (2016). Strict convexity and the regularity of solutions to variational problems. ESAIM. COCV, 22(3), 862-871 [10.1051/cocv/2015034].
Strict convexity and the regularity of solutions to variational problems
CELLINA, ARRIGO
2016
Abstract
We consider the problem of minimizing {equation presented} where Ω is a bounded open subset of RN and L is a convex function that grows quadratically outside the unit ball, while, when |∇ν| < 1, it behaves like |∇ν|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 {equation presented} in particular, for every i = 1, ...N, we have max {equation presented}.
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