A note on improved differentiability for the banach-space valued finsler γ-laplacian

SUMMARY

For all p, q ≥ 0, p-q ¡ ¢ F ∆h Vp,q (∇u) ~ (F (∇u) + F (∇u h )) q F (∆h ∇u). So implies ¡ ¢q F ∆h Vp,q (∇u) ~ (F (∇u) + F (∇u h ))p-q F (∆h ∇u)q ≥ F (∆h u)p, confirming. p-q Suppose p ≤ q. η ∈ C c (Ω) and A=spt η. α α ′ ′,τ γ σ τ V (∇u) ∈ B∞,loc (Ω) and V * ( j F (∇u)) ∈ B∞,loc (Ω) The authors write Z I= γ Ω 〈∆h j F (∇u), ηβ ∆h ∇u〉X⊗Rn + β Z γ Ω ηβ-1 〈∆h j F (∇u), ∆h u ⊗ ∇η〉=: A 1 + A 2. The authors return to, choose β=γ ≥ σ ≥ 2 . . .

 



If you want to have access to all the content you need to log in!

Thanks :)

Username or Email

Password

Remember me

Lost your password?

If you don't have an account, you can create one here.