2021/09/10 by Mouhamed Moustapha Fall, Tadele Mengesha, Fall, Mouhamed Moustapha +5
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations
paper · pdf · doi:10.48550/arxiv.2109.04879
openalex publication_date 2021/09/10 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Given 2\≤ p<\∞, s\∈ (0, 1) and t\∈ (1, 2s), we establish\ninterior Wt,p Calderon-Zygmund estimates for solutions of nonlocal\nequations of the form n
int
Omega
int
Omega K
left (x,|x-y|,
fracx-y|x-y|
right )\n
frac(u(x)-u(y))(
varphi(x)-
varphi(y))|x-y|n+2s dx dy = g[
varphi],\n
quad
forall
phi
in Cc
infty(
Omega) where \Ω\⊂\n\ℝn is an open set.\n Here we assume K is bounded, nonnegative and continuous in the first entry\n-- and ellipticity is ensured by assuming that K is strictly positive in a\ncone.\n The setup is chosen so that it is applicable for nonlocal equations on\nmanifolds, but the structure of the equation is general enough that it also\napplies to the certain fractional p-Laplace equations around points where u\n\∈ C1 and |\∇ u| \≠ 0.\n