Related papers: Pseudo-Taylor expansions and the Carath\'{e}odory-…

In this paper we prove mesh independent a priori $L^\infty$-bounds for positive solutions of the finite difference boundary value problem $$ -\Delta_h u = f(x,u) \mbox{ in } \Omega_h, \quad u=0 \mbox{ on } \partial\Omega_h, $$ where…

In this work, we prove the existence of a positive solution to the second-order nonlinear problem $u''+f(t,u,u')=0$ with mixed boundary conditions, where $f$ is an $L^p$-Carath\'eodory function satisfying certain properties. Three boundary…

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…

We give a formula for the Carath\'eodory distance on the Neil parabola, the variety ${z^2=w^3}$ restricted to the bidisk; thus making it the first variety with a singularity to have its Carath\'eodory distance explicitly computed. In…

We analyze general convergence properties of the Taylor expansion of observables to finite chemical potential in the framework of an effective 2+1 flavor Polyakov-quark-meson model. To compute the required higher order coefficients a novel…

Let $\bx_j = \btheta +\bep_j, j=1,...,n$, be observations of an unknown parameter $\btheta$ in a Euclidean or separable Hilbert space $\scrH$, where $\bep_j$ are noises as random elements in $\scrH$ from a general distribution. We study the…

The Julia quotient measures the ratio of the distance of a function value from the boundary to the distance from the boundary. The Julia-Carath\'eodory theorem on the bidisk states that if the Julia quotient is bounded along some sequence…

In this work, first we prove that for any compact set $K\subset\mathbb{R}^{n}$ and any continuous function $\phi$ defined on $\partial K$, there exists a bounded weak solution in $C(\bar{\mathbb{R}^{n}\backslash K}) \cap…

We develop arguments on convexity and minimization of energy functionals on Orlicz-Sobolev spaces to investigate existence of solution to the equation $\displaystyle -\mbox{div} (\phi(|\nabla u|) \nabla u) = f(x,u) + h \mbox{in} \Omega$…

This paper develops an abstract theory for subdifferential operators to give existence and uniqueness of solutions to the initial-boundary problem (P) for the nonlinear diffusion equation in an unbounded domain $\Omega\subset\mathbb{R}^N$…

We analyze and test using Fourier extensions that minimize a Hilbert space norm for the purpose of solving partial differential equations (PDEs) on surfaces. In particular, we prove that the approach is arbitrarily high-order and also show…

We determine the curvature of the pseudo-critical line of $N_f = 2 + 1$ QCD with physical quark masses via Taylor expansion in the quark chemical potentials. We adopt a discretization based on stout improved staggered fermions and the tree…

The validity of the von-Neumann inequality for commuting $n$ - tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the…

We demonstrate a lower bound technique for linear decision lists, which are decision lists where the queries are arbitrary linear threshold functions. We use this technique to prove an explicit lower bound by showing that any linear…

In this paper, we consider the following nonlinear parabolic equation with non-coercive terms in \(R^N\) space \[ \dfrac{\partial u}{\partial t} -\nabla \cdot (a(x,t,u,\nabla u)+ \Phi(x,t,\nabla u))=f, \text{ in }\Omega \times (0,T). \]…

Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature. The implementation of this…

We describe a generalization of the notion of a Hilbert space model of a function $\varphi$ in the Schur-Agler class of the polydisc. This generalization is well adapted to the investigation of boundary behavior of $\varphi$ at a mild…

This paper is an exposition, with some new applications, of our results on the growth of entropy of convolutions. We explain the main result on $\mathbb{R}$, and derive, via a linearization argument, an analogous result for the action of…

The textbook adversary bound for function evaluation states that to evaluate a function $f\colon D\to C$ with success probability $\frac{1}{2}+\delta$ in the quantum query model, one needs at least $\left( 2\delta -\sqrt{1-4\delta^2}…

We consider a particle living in $\mathbb{R}_+$, whose velocity is a positive recurrent diffusion with heavy-tailed invariant distribution when the particle lives in $(0,\infty)$. When it hits the boundary $x=0$, the particle restarts with…