Regularity results for a class of non-differentiable obstacle problems. (May 2020) - Eleuteri, Michela; Passarelli di Napoli, Antonia
Abstract: In this paper we prove the higher differentiability in the scale of Besov spaces of the solutions to a class of obstacle problems of the type min ∫ Ω F ( x, z, D z ) : z ∈ K ψ ( Ω ) . Here Ω is an open bounded set of R n, n ≥ 2, ψ is a fixed function called obstacle and K ψ ( Ω ) is set of admissible functions z ∈ W 1, p ( Ω ) such that z ≥ ψ a.e. in Ω . We assume that the gradient of the obstacle belongs to a suitable Besov space. The main novelty here is that we are not assuming any differentiability on the partial maps x ↦ F ( x, z, D z ) and z ↦ F ( x, z, D z ), but only their Hölder continuity.