Displaying similar documents to “Behaviour of solutions to the Dirichlet problem for the biharmonic operator at a boundary point”

Regularity results for a class of obstacle problems in Heisenberg groups

Francesco Bigolin (2013)

Applications of Mathematics

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We study regularity results for solutions u ∈ H W 1 , p ( Ω ) to the obstacle problem ∫ Ω 𝒜 ( x , ∇ ℍ u ) ∇ ℍ ( v - u ) d x ≥ 0 ∀ v ∈ 𝒦 ψ , u ( Ω ) such that u ≥ ψ a.e. in Ω , where 𝒦 ψ , u ( Ω ) = { v ∈ H W 1 , p ( Ω ) : v - u ∈ H W 0 1 , p ( Ω ) v ≥ ψ a.e. in Ω } , in Heisenberg groups ℍ n . In particular, we obtain weak differentiability in the T -direction and horizontal estimates of Calderon-Zygmund type, i.e. d T ψ ∈ H W loc 1 , p ( Ω ) ⇒ T u ∈ L loc p ( Ω ) , | ∇ ℍ ψ | p ∈ L loc q ( Ω ) ⇒ | ∇ ℍ u | p ∈ L loc q ( Ω ) , d where 2 < p < 4 , q > 1 .