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Given $2leq p<infty$, $sin (0, 1)$ and $tin (1, 2s)$, we establish interior $W^{t,p}$ Calderon-Zygmund estimates for solutions of nonlocal equations of the form [ int_{Omega} int_{Omega} Kleft (x,|x-y|,frac{x-y}{|x-y|}right ) frac{(u(x)-u(y))(varphi(x)-varphi(y))}{|x-y|^{n+2s}} dx dy = g[varphi], quad forall phiin C_c^{infty}(Omega) ] where $Omegasubset mathbb{R}^{n}$ is an open set. Here we assume $K$ is bounded, nonnegative and continuous in the first entry -- and ellipticity is ensured by assuming that $K$ is strictly positive in a cone. The setup is chosen so that it is applicable for nonlocal equations on manifolds, but the structure of the equation is general enough that it also applies to the certain fractional $p$-Laplace equations around points where $u in C^1$ and $| abla u| eq 0$.
We study interior $L^p$-regularity theory, also known as Calderon-Zygmund theory, of the equation [ int_{mathbb{R}^n} int_{mathbb{R}^n} frac{K(x,y) (u(x)-u(y)), (varphi(x)-varphi(y))}{|x-y|^{n+2s}}, dx, dy = langle f, varphi rangle quad varphi in C
We deal with a global Calderon-Zygmund type estimate for elliptic obstacle problems of $p$-Laplacian type with measure data. For this paper, we focus on the singular case of growth exponent, i.e. $1<p le 2-frac{1}{n}$. In addition, the emphasis of th
We represent a bilinear Calderon-Zygmund operator at a given smoothness level as a finite sum of cancellative, complexity zero operators, involving smooth wavelet forms, and continuous paraproduct forms. This representation results in a sparse $T(1)$
We present a new method for the existence and pointwise estimates of a Greens function of non-divergence form elliptic operator with Dini mean oscillation coefficients. We also present a sharp comparison with the corresponding Greens function for constant coefficients equations.
This paper is concerned with existence of viscosity solutions of non-translation invariant nonlocal fully nonlinear equations. We construct a discontinuous viscosity solution of such nonlocal equation by Perrons method. If the equation is uniformly e