A gradient bound for free boundary graphs

A Gradient Bound for Free Boundary Graphs

We prove an analogue for a one-phase free boundary problem of the classical gradient bound for solutions to the minimal surface equation. It follows, in particular, that every energy-minimizing free boundary that is a graph is also smooth. The method we use also leads to a new proof of the classical mimimal surface gradient bound.

Vizing's conjecture: A two-thirds bound for claw-free graphs

Preconditioned Conjugate Gradient Method for Boundary Artifact-Free Image Deblurring

Several methods have been proposed to reduce boundary artifacts in image deblurring. Some of those methods impose certain assumptions on image pixels outside the field-of-view; the most important of these assume reflective or anti-reflective boundary conditions. Boundary condition methods, including reflective and anti-reflective ones, however, often fail to reduce boundary artifacts, and, in s...

K5-Free bound for the class of planar graphs

We define k-diverse colouring of a graph to be a proper vertex colouring in which every vertex x, sees min{k, d(x)} different colours in its neighbors. We show that for given k there is an f(k) for which every planar graph admits a k-diverse colouring using at most f(k) colours. Then using this colouring we obtain a K5-free graph H for which every planar graph admits a homomorphism to it, thus ...

A bound for Feichtinger conjecture

In this paper‎, ‎using the discrete Fourier transform in the finite-dimensional Hilbert space C^n‎, ‎a class of nonRieszable equal norm tight frames is introduced ‎and‎ using this class, a bound for Fiechtinger Conjecture is presented. By the Fiechtinger Conjecture that has been proved recently, for given A,C>0 there exists a universal constant delta>0 independent of $n$ such that every C-equal...