ISSN: 1314-3344
Miaomiao JIA
In this paper we deal with the problem u ∈ Cψ(â¦), ∀ ω ∈ Cψ(â¦), Z ⦠f(x, Du)dx ≤ Z ⦠f(x, Dω)dx, where Cψ(â¦) = {w ∈ u∗ + W 1,(pi) 0 (â¦) such that x → f(x, Dw) ∈ L 1 (â¦), w ≥ ψ, a.e. â¦}. We consider a minimizer u : ⦠⊂ Rn → R among all functions that agree on the boundary ∂⦠with some fixed boundary value u∗. And we assume that the function θ = max{u∗, ψ} makes the density f(x, Du) more integrable under the obstacle problem and we prove that the minimizer u enjoy higher integrability.