Related papers: Gradient Bounds and Coarsening Estimates for Some …

We continue our study on the global solution to the two-dimensional Prandtl's system for unsteady boundary layers in the class considered by Oleinik provided that the pressure is favorable. First, by using a different method from [13], we…

Consider positive solutions to second order elliptic equations with measurable coefficients in a bounded domain, which vanish on a portion of the boundary. We give simple necessary and sufficient geometric conditions on the domain, which…

We prove quantitative growth estimates for large data solutions to the 1D Boltzmann equation, for a collision kernel with angular cutoff and relative velocity cutoff. We present proofs for the global well-posedness results presented in the…

We study, using noise reduction techniques, layer by layer epitaxial growth in limited mobility solid-on-solid nonequilibrium surface growth models, which have been introduced in the context of kinetic surface roughening in ideal molecular…

Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the Ehrlich-Schwoebel effect, Siegert et al \cite{Siegert94} formulate a model of Langevin type that describes the growth of pyramidlike…

We present a simple model which allows to investigate equilibrium aspects of molecular recognition between rigid biomolecules on a generic level. Using a two-stage approach, which consists of a design and a testing step, the role of…

We establish several bounds for solutions to elliptic/parabolic cross-diffusion systems of $m$ equations ($m\ge2$) on 2d/3d domains $\Og$. We settle the existence and global existence problems in these cases and also provide new…

In this work we establish a gradient bound and Liouville-type theorems for solutions to Quasi-linear elliptic equations on compact Riemannian Manifolds with nonnegative Ricci curvature. Also, we provide a local splitting theorem when the…

We prove existence of thick geodesic triangulations of hyperbolic 3-manifolds and use this to prove existence of universal bounds on the principal curvatures of surfaces embedded in hyperbolic 3-manifolds.

Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…

In this paper we show existence of solutions for some elliptic problems with nonlocal diffusion by means of nonvariational tools. Our proof is based on the use of topological degree, which requires a priori bounds for the solutions. We…

We establish sharp geometric Holder regularity estimates for Gradient for bounded solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy. Such regularity estimates simplify and generalize, to some extent,…

We give theorems that can be used to upper bound the densities of packings of different spherical caps in the unit sphere and of translates of different convex bodies in Euclidean space. These theorems extend the linear programming bounds…

An approximation is elaborated for the paraxial propagation of diffracted beams, with both one- and two-dimensional cross sections, which are released from apertures with sharp boundaries. The approximation applies to any beam under the…

Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that…

This paper is concerned with the existence and the regularity of global solutions to the linear wave equation associated with two-point type boundary conditions. We also investigate the decay properties of the global solutions to this…

Global solution curve and exact multiplicity of positive solutions for a class of fourth-order beam equations with clamped boundary conditions are derived. The results extend atheorem of P. Korman (2004) by allowing the presence of a…

We establish local elliptic and parabolic gradient estimates for positive smooth solutions to a nonlinear parabolic equation on a smooth metric measure space. As applications, we determine various conditions on the equation's coefficients…

In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to Dirichlet and Neumann problems of a class of Schr\"odinger equations under the minimal…

We have developed in the past several algorithms with intrinsic complexity bounds for the problem of point finding in real algebraic varieties. Our aim here is to give a comprehensive presentation of the geometrical tools which are…