Related papers: Bootstrap regularity for integro-differential oper…

We consider an elliptic equation with the fractional Laplacian operator $(-\Delta)^{\frac{\alpha}{2}}$ in the dissipative term, a singular integral operator ${\bf A}(\cdot)$ in the nonlinear term, and an external source $f$. The key example…

We prove that, if a Brakke flow with boundary is close enough to a stationary half-plane with density one, then it is $C^{1,\alpha}$. Our approach is based on viscosity techniques introduced by Savin in the context of elliptic equations.…

We show that the spectral radius for the action of a self map $f$ of a smooth projective variety (over an arbitrary base field) on its $\ell$-adic cohomology is achieved on the $f^*$-stable sub-algebra generated by any ample class. This…

For the open unit disc $\mathbb{D}$ in the complex plane, it is well known that if $\phi \in C(\overline{\mathbb{D}})$ then its Berezin transform $\widetilde{\phi}$ also belongs to $C(\overline{\mathbb{D}})$. We say that $\mathbb{D}$ is…

We study approximability of regular constraint satisfaction problems, i.e., CSPs where each variable in an instance has the same number of occurrences. In particular, we show that for any CSP $\Lambda$, existence of an $\alpha$…

We continue our investigations into Toda's algorithm [14,3]; a Weierstrass-type representation of Gauss curvature $K=-1$ surfaces in $\mathbb{R}^3$. We show that $C^0$ input potentials correspond in an appealing way to a special new class…

We develop an approach to construct local bulk operators in a CFT to order $1/N^2$. Since 4-point functions are not fixed by conformal invariance we use the OPE to categorize possible forms for a bulk operator. Using previous results on…

We prove well-posedness for some abstract differential equations of the first order. Our result covers the usual case of Lipschitz composition operators. It also contains the case of some integro-differential operators acting on spaces with…

Consider $A(x,D):C^{\infty}(\Omega,E) \rightarrow C^\infty(\Omega,F)$ an elliptic and canceling linear differential operator of order $\nu$ with smooth complex coefficients in $\Omega \subset \mathbb{R}^{N}$ from a finite dimension complex…

In this paper we prove quantitative regularity results for stationary and minimizing extrinsic biharmonic maps. As an application, we determine sharp, dimension independent $L^p$ bounds for $\nabla^k f$ that do not require a small energy…

We prove the optimal global regularity of nonnegative solutions to the porous medium equation in smooth bounded domains with the zero Dirichlet boundary condition after certain waiting time $T^*$. More precisely, we show that solutions are…

We prove a multi-valued $C^{1,\alpha}$ regularity theorem for the varifolds in the class $\mathcal{S}_2$ (i.e., stable codimension one stationary integral $n$-varifolds admitting no triple junction classical singularities) which are…

In this article we extend a previous definition of Castelnuovo-Mumford regularity for modules over an algebra graded by a finitely generated abelian group. Our notion of regularity is based on Maclagan and Smith's definition, and is…

Given a $C^k$-smooth closed embedded manifold $\mathcal N\subset{\mathbb R}^m$, with $k\ge 2$, and a compact connected smooth Riemannian surface $(S,g)$ with $\partial S\neq\emptyset$, we consider $\frac 12$-harmonic maps $u\in…

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 establish local regularity results for minimizers of autonomous vectorial integrals of Calculus of Variations, assuming $\psi$-growth conditions and imposing $\varphi$-quasiconvexity only in an asymptotic sense, both in the sub-quadratic…

We establish regularity results for critical points to energies of immersed surfaces depending on the first and the second fundamental form exclusively. These results hold for a large class of intrinsic elliptic Lagrangians which are…

We study the automorphism group of a unital, simple, $\mathcal{Z}$-stable $C^{*}$-algebra. In this paper, we generalize the results by the authors in \cite{pr_auto} to $\mathcal{Z}$-stable $C^{*}$-algebras $\mathfrak{A}$ such that…

In this paper we prove the higher Sobolev regularity of minimisers for convex integral functionals evaluated on linear differential operators of order one. This intends to generalise the already existing theory for the cases of full and…

In this note we study the boundary regularity of solutions to nonlocal Dirichlet problems of the form $Lu=0$ in $\Omega$, $u=g$ in $\mathbb R^N\setminus\Omega$, in non-smooth domains $\Omega$. When $g$ is smooth enough, then it is easy to…