Wang, Zhenqiang2023-04-252023-04-252022-08-22Wang, Z. (2022). Higher differentiability for solutions to nonhomogeneous obstacle problems with 1<p<2. <i>Electronic Journal of Differential Equations, 2022</i>(62), pp. 1-28.1072-6691https://hdl.handle.net/10877/16652In this article, we establish integer and fractional higher-order differentiability of weak solutions to non-homogeneous obstable problems that satisfy the variational inequality ∫Ω ‹A(x, Du), D(φ - u)› dx ≥ ∫Ω ‹|F|p-2 F, D(φ - u)› dx, where 1 < p < 2, φ ∈ Kψ(Ω) = {v ∈ u0 + W1,p 0 (Ω, ℝ) : v ≥ ψ a.e. in Ω}, u0 ∈ W1,p(Ω) is a fixed boundary datum. We show that the weak solution, provided the partial map x ↦ A(x, ξ) belongs to a suitable Sobolev or Besov-Lipschitz space.Text28 pages1 file (.pdf)enAttribution 4.0 InternationalNonhomogeneous elliptic obstacle problemsHigher differentiabilitySobolev coefficientsBesov-Lipschitz coefficientsArticle