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We prove that the weak solution of a uniformly elliptic stochastic differential equation with locally smooth diffusion coefficient and H\"{o}lder continuous drift has a H\"{o}lder continuous density f...
Let $\lambda_{q}:=\inf{\Vert\nabla u\Vert_{L^{p}(\Omega)}^{p}/\Vertu\Vert_{L^{q}(\Omega)}^{p}:u\in W_{0}^{1,p}(\Omega)\setminus{0}} $, where $\Omega$ is a bounded and smooth domain of $\mathbb{R}^{N},...
Recently, M.\ Ab\'ert and T.\ Hubai studied the following problem. The chromatic measure of a finite simple graph is defined to be the uniform distribution on its chromatic roots. Ab\'ert and Hubai pr...
We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborho...
Abstract: We show that in $\mathbb{C}^2$ if the set of strongly regular points are closed in the boundary of a smooth bounded pseudoconvex domain, then the domain is c-regular, that is, the plurisubha...
Abstract: This paper concerns the question whether the cone spectral radius of a continuous compact order-preserving homogenous map on a closed cone in Banach space depends continuously on the map. Us...
Abstract: Consider transportation of one distribution of mass onto another, chosen to optimize the total expected cost, where cost per unit mass transported from x to y is given by a smooth function c...
Abstract: We show how the $A_\infty$ class of weights can be considered as a metric space. As far as we know this is the first time that a metric d is considered on this set. We use this metric to gen...
Abstract: We extend our Nevanlinna-Pick theorem for Hardy algebras and their representations to cover interpolation at the absolutely continuous points of the boundaries of their discs of representati...
We study continuity and regularity of convex extensions of functions from a compact set C to its convex hull K = co(C). We show that if C contains the relative boundary of K, and f is a continuous con...
We prove that for harmonic quasiconformal mappings -H¨older continuity on the boundary implies -H¨older continuity of the map itself. Our result holds for the class of uniformly perfect bounded doma...
In this paper, we study the behavior of Ricci-flat K¨ahler metrics on Calabi-Yau manifolds under algebraic geometric surgeries: extremal transitions or flops. We prove a version of Candelas and de la ...
This is a continuation of paper [7]. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Amp`ere e...
We discuss the ideal-adic semi-continuity problem for minimal log discrepancies by Mustat¸˘a. We study the purely log terminal case, and prove the semi-continuity of minimal log discrepanci...
The integrated density of states of a Schr¨odinger operator with random potential given by a homogeneous Gaussian field whose covariance function is continuous, compactly supported and has positive me...

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