Related papers: $C^{\sigma+\alpha}$ regularity for concave nonloca…

We prove a $C^{1,\alpha}$ interior regularity theorem for fully nonlinear uniformly elliptic integro-differential equations without assuming any regularity of the kernel. We then give some applications to linear theory and higher regularity…

We prove space and time regularity for solutions of fully nonlinear parabolic integro-differential equations with rough kernels. We consider parabolic equations $u_t = \I u$, where $\I$ is translation invariant and elliptic with respect to…

We obtain Dini type estimates for a class of concave fully nonlinear nonlocal elliptic equations of order $\sigma\in (0,2)$ with rough and non-symmetric kernels. The proof is based on a novel application of Campanato's approach and a…

We prove a priori interior $C^{2,\alpha}$ estimates for solutions of fully nonlinear elliptic equations of twisted type. For example, our estimates apply to equations of the type convex + concave. These results are particularly well suited…

We establish sharp $C^{2s}$ interior regularity estimates for solutions of fully nonlinear nonlocal equations with bounded right hand side. More precisely, we show that if $I$ is a fully nonlinear nonlocal concave or convex elliptic…

Given a concave integro-differential operator $I$, we study regularity for solutions of fully nonlinear, nonlocal, parabolic, concave equations of the form $u_t-Iu=0$. The kernels are assumed to be smooth but non necessarily symmetric which…

We establish sharp regularity estimates for solutions to $Lu=f$ in $\Omega\subset\mathbb R^n$, being $L$ the generator of any stable and symmetric L\'evy process. Such nonlocal operators $L$ depend on a finite measure on $S^{n-1}$, called…

We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear…

In this article, we prove the local $C^{0,\alpha}$ regularity and provide $C^{0,\alpha}$ estimates for viscosity solutions of fully nonlinear, possibly degenerate, elliptic equations associated to linear or nonlinear Neumann type boundary…

In this paper, we establish $C^{1, \alpha}$ regularity upto the boundary for a class of degenerate fully nonlinear elliptic equations with Neumann boundary conditions. Our main result Theorem 2.1 constitutes the boundary analogue of the…

We obtain Schauder estimates for a class of concave fully nonlinear nonlocal parabolic equations of order $\sigma\in (0,2)$ with rough and non-symmetric kernels. As a application, we prove that the solution to a translation invariant…

We establish the interior $C^{1,\alpha}$-estimate for viscosity solutions of degenerate/singular fully nonlinear parabolic equations $$u_t = |Du|^{\gamma}F(D^2u) + f.$$ For this purpose, we prove the well-posedness of the regularized…

We study interior $C^{2,\alpha}$ regularity estimates for solutions of fully nonlinear uniformly elliptic equations of the general form $F(D^2u)=0$ in two independent variables and without any geometric condition on $F$. By means of the…

This article is concerned with ``up to $C^{2, \alpha}$-regularity results'' about a mixed local-nonlocal nonlinear elliptic equation which is driven by the superposition of Laplacian and fractional Laplacian operators. First of all, an…

We establish higher regularity properties of solutions to fully nonlinear elliptic equations at interior critical points. The key novelty of our estimates lies in the fact that they yield smoothness properties that go beyond the inherent…

We study the regularity of solutions to the fully nonlinear thin obstacle problem. We establish local $C^{1,\alpha}$ estimates on each side of the smooth obstacle, for some small $\alpha > 0$. Our results extend those of Milakis-Silvestre…

We give sharp $C^{2,\alpha}$ estimates for solutions of some fully nonlinear elliptic and parabolic equations in complex geometry and almost complex geometry, assuming a bound on the Laplacian of the solution. We also prove the analogous…

We prove optimal boundary $C^{1,\alpha}$ regularity for viscosity solutions of degenerate fully nonlinear uniformly elliptic equations with oblique boundary conditions and Hamiltonian terms of the form \[ \begin{cases} |Du|^{\gamma}F(D^2 u)…

We establish sharp boundary regularity estimates in $C^1$ and $C^{1,\alpha}$ domains for nonlocal problems of the form $Lu=f$ in $\Omega$, $u=0$ in $\Omega^c$. Here, $L$ is a nonlocal elliptic operator of order $2s$, with $s\in(0,1)$.…

We study the higher H\"older regularity of local weak solutions to a class of nonlinear nonlocal elliptic equations with kernels that satisfy a mild continuity assumption. An interesting feature of our main result is that the obtained…