2024/01/03 by Tadele Mengesha, Armin Schikorra, Mengesha, Tadele +5
Engineering · Mathematics · #Numerical methods in engineering #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2401.01886
We extend the Calderón-Zygmund theory for nonlocal equations to strongly coupled system of linear nonlocal equations LsA u = f, where the operator LsA is formally given by LsAu = ∫ℝn\fracA(x, y)\vert x-y\vert n+2s ((x-y)⊗ (x-y))/(\vert x-y\vert 2)(u(x)-u(y))dy. For 0 < s < 1 and A:ℝn × ℝn → ℝ taken to be symmetric and serving as a variable coefficient for the operator, the system under consideration is the fractional version of the classical Navier-Lamé linearized elasticity system. The study of the coupled system of nonlocal equations is motivated by its appearance in nonlocal mechanics, primarily in peridynamics. Our regularity result states that if A(⋅, y) is uniformly Holder continuous and infx∈ ℝnA(x, x) > 0, then for f∈ Lploc, for p≥ 2, the solution vector u∈ H2s-δ,ploc for some δ∈ (0, s).