Higher differentiability for solutions to nonhomogeneous obstacle problems with 1<p<2
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Date
2022-08-22
Authors
Wang, Zhenqiang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
In 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.
Description
Keywords
Nonhomogeneous elliptic obstacle problems, Higher differentiability, Sobolev coefficients, Besov-Lipschitz coefficients
Citation
Wang, 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.
Rights
Attribution 4.0 International