Related papers: $C^{1,1}$ regularity for principal-agent problems
We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries are $C^{1,\text{Dini}}$ and $C^{\gamma_{0}}$ in the spatial…
We prove $C^1$ regularity of solutions to divergence form elliptic systems with Dini-continuous coefficients
Recently I. Capuzzo Dolcetta, F. Leoni and A. Porretta obtain a very surprising regularity result for fully nonlinear, superquadratic, elliptic equations by showing that viscosity subsolutions of such equations are locally H\"older…
We consider critical points of the geometric obstacle problem on vectorial maps $u: \mathbb{B}^2 \subset \mathbb{R}^2 \to \mathbb{R}^N$ \[ \int_{\mathbb{B}^2} |\nabla u|^2 \quad \mbox{subject to $u \in \mathbb{R}^N \backslash…
In this paper we study geometrical and dynamical properties of codimension one foliations, by exploring a relation between length averages and ball averages of certain group actions. We introduce a new mechanism, which relies on the group…
In this paper we slightly improve the regularity theory for the so called optimal design problem. We first establish the uniform rectifiability of the boundary of the optimal set, for a larger class of minimizers, in any dimension. As 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 classic principal-agent model when the signal observed by the principal is chosen by the agent. We fully characterize the optimal information structure from an agent's perspective in a general moral hazard setting with limited…
Regularity theorems \`a la Avellaneda-Lin are an indispensable part of the modern quantitative theory of stochastic homogenization. While interior regularity results for random elliptic operators have been available for a while, on general…
We address the question of the exponential stability for the $C^{1}$ norm of general 1-D quasilinear systems with source terms under boundary conditions. To reach this aim, we introduce the notion of basic $C^{1}$ Lyapunov functions, a…
We prove local Lipschitz regularity for local minimiser of \[ W^{1,1}(\Omega)\ni v\mapsto \int_\Omega F(Dv)\, dx \] where $\Omega\subseteq {\mathbb R}^N$, $N\ge 2$ and $F:{\mathbb R}^N\to {\mathbb R}$ is a quasiuniformly convex integrand in…
In this paper we study a generalization of the continuous time Principal-Agent problem allowing for time inconsistent utility functions, for instance of mean-variance type. Using recent results on the Pontryagin maximum principle for FBSDEs…
The purpose of this note is to give a complete proof of a $C^{0,\alpha}$ regularity result for the pressure for weak solutions of the two-dimensional "incompressible Euler equations" when the fluid velocity enjoys the same type of…
In this paper, we study the regularity for viscosity solutions of locally uniformly elliptic equations and obtain a series of interior pointwise $C^{k,\alpha}$ ($k\geq 1$, $0<\alpha<1$) regularity with smallness assumptions on the solution…
We study the satisfiability of ordering constraint satisfaction problems (CSPs) above average. We prove the conjecture of Gutin, van Iersel, Mnich, and Yeo that the satisfiability above average of ordering CSPs of arity $k$ is…
The key point to prove the optimal $C^{1,\frac12}$ regularity of the thin obstacle problem is that the frequency at a point of the free boundary $x_0\in\Gamma(u)$, say $N^{x_0}(0^+,u)$, satisfies the lower bound $N^{x_0}(0^+,u)\ge\frac32$.…
We establish Ambrosetti -Prodi type results for periodic solutions of one -dimensional nonlinear problems with drift term and drift -less whose principal operator is the fractional Laplacian of order $s\in(0,1)$. We establish conditions for…
In this paper, we study the optimal regularity of the stationary sonic-subsonic solution to the unipolar isothermal hydrodynamic model of semiconductors with sonic boundary. Applying the comparison principle and the energy estimate, we…
This work proposes a unified theory of regularity in one hypercomplex variable: the theory of $T$-regular functions. In the special case of quaternion-valued functions of one quaternionic variable, this unified theory comprises…
In this article we investigate the solution of the steady-state fractional diffusion equation on a bounded domain in $\real^{1}$. From an analysis of the underlying model problem, we postulate that the fractional diffusion operator in the…