An extension of Alberti's result to second order derivatives is obtained. Precisely, if Ω is an open subset of ℝN and if f ∈ L1(Ω; ℝN × N)) is symmetric-valued, then there exist u ∈ W1,1 (Ω) with ∇u ∈ BV(Ω ℝN) and a constant C > 0 depending only on N such that D 2u = f ℒN [Ω + [∇u] ⊗ ν∇u ℋN-1 ∫ S(∇u), and ∫Ω |u|+ |∇u|dx + ∫s(∇u) |[∇u]|dℋN-1 ≤ C ∫Ω |f| dx.
On Hessian matrices in the space BH
Paroni, Roberto
2005-01-01
Abstract
An extension of Alberti's result to second order derivatives is obtained. Precisely, if Ω is an open subset of ℝN and if f ∈ L1(Ω; ℝN × N)) is symmetric-valued, then there exist u ∈ W1,1 (Ω) with ∇u ∈ BV(Ω ℝN) and a constant C > 0 depending only on N such that D 2u = f ℒN [Ω + [∇u] ⊗ ν∇u ℋN-1 ∫ S(∇u), and ∫Ω |u|+ |∇u|dx + ∫s(∇u) |[∇u]|dℋN-1 ≤ C ∫Ω |f| dx.File in questo prodotto:
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