Related papers: Upper bound for the Lempert function of smooth dom…

We construct the upper and lower Bellman functions for the $L^p$ (quasi)-norms of BMO functions. These appear as solutions to a series of Monge--Amp\`ere boundary value problems on a non-convex plane domain. The knowledge of the Bellman…

We prove \emph{uniform solvability estimates} for certain families of elliptic problems posed in a bounded family of domains (for example, a sequence that converges to another domain). We provide uniform estimates both in weighted and in…

We show subellipticity of the d-bar Neumann problem on domains with Lipschitz boundary in the presence of plurisubharmonic functions with Hessians of algebraic growth. In particular, a subelliptic estimate holds near a point where the…

We consider mesh functions which are discrete convex in the sense that their central second order directional derivatives are positive. Analogous to the case of a uniformly bounded sequence of convex functions, we prove that the uniform…

We establish the slope equality and give an upper bound of the slope for finite cyclic covering fibrations of an elliptic surface including bielliptic fibrations of genus greater than 5. We also give an upper bound of the slope for triple…

This paper studies the Neumann boundary value problems for the Stokes equations in a convex domain in $\mathbb{R}^d$. We obtain nontangential-maximal-function estimates in $L^p$ and $W^{1, p}$ estimates for $p$ in certain ranges depending…

In this paper, we establish sharp upper bounds on shifted moments of the family of Dirichlet $L$-functions to a fixed modulus over function fields. We apply the result to obtain upper bounds on moments of Dirichlet character sums over…

In this paper we prove asymptotic upper bounds on the variance of the number of vertices and missed area of inscribed random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We also consider a circumscribed variant of this…

In this paper, we obtain uniform bounds for a number of expressions that involve derivatives and integrals of modified Bessel functions. These uniform bounds are motivated by the need to bound such expressions in the study of variance-gamma…

In this paper we present an extension of known semidefinite and linear programming upper bounds for spherical codes and consider a version of this bound for distance graphs. We apply the main result for the distance distribution of a…

We give asymptotics for the level set equation for mean curvature flow on a convex domain near the point where it attains a maximum. It is known that solutions are not necessarily $C^3,$ and we recover this result and construct non-smooth…

This paper is devoted to the proof of Lipschitz regularity, down to the microscopic scale, for solutions of an elliptic system with highly oscillating coefficients, over a highly oscillating Lipschitz boundary. The originality of this…

We show that for any uniformly elliptic fully nonlinear second-order equation with bounded measurable "coefficients" and bounded "free" term one can find an approximating equation which has a unique continuous and having the second…

We give explicit isoperimetric upper bounds for all Steklov eigenvalues of a compact orientable surface with boundary, in terms of the genus, the length of the boundary, and the number of boundary components. Our estimates generalize a…

We prove new endpoint bounds for the lacunary spherical maximal operator and as a consequence obtain almost everywhere pointwise convergence of lacunary spherical means for functions locally in $L\log\log\log L(\log\log\log\log…

Let $\mathcal{N}\mathcal{F}$ be the class of smooth non-flat curves near the origin and near infinity previously introduced by the second author and let $\gamma\in\mathcal{N}\mathcal{F}$. We show - via a unifying approach relative to the…

We obtain a universal energy estimate up to the boundary for stable solutions of semilinear equations with variable coefficients. Namely, we consider solutions to $- L u = f(u)$, where $L$ is a linear uniformly elliptic operator and $f$ is…

We find explicit and optimal upper bounds for the expected occupation density for an It\^o-process when its drift and diffusion coefficients are unknown under boundedness and ellipticity conditions on the coefficients. This is related to…

For smooth bounded domains in $\mathbb{R}$, we prove upper and lower $L^2$ bounds on the boundary data of Neumann eigenfunctions, and prove quasi-orthogonality of this boundary data in a spectral window. The bounds are tight in the sense…

In this note we present upper bounds for the variational eigenvalues of the $p$-Laplacian on smooth domains of complete $n$-dimensional Riemannian manifolds and Neumann boundary conditions, and on compact (boundaryless) Riemannian…