数学学报杂志 北大期刊 CSCD期刊 统计源期刊

Special Issue in Honor of Professor Carlos E. Kenig

作者：Guozhen; Lu; Zhongwei; Shen 刊期：2019年第06期

It is our great honor and pleasure to be the guest editors for this special issue of the Acta Mathematica Sinica-English Series, a flagship journal of the Chinese Mathematical Society, dedicated to Professor Carlos E. Kenig from the University of Chicago on the occasion of his 65th birthday.

Three Problems on Trigonometric Sums

作者：Yves; MEYER 刊期：2019年第06期

Let Λ ■R~n be a uniformly discrete set and let C_Λ be the vector space consisting of all mean periodic functions whose spectrum is simple and contained in Λ. If Λ is a gentle set then for every f ∈ C_Λ we have f(x) = O(ω_Λ(x)) as |x| →∞ and ω_Λ(x) can be estimated(Theorem 4.1). This line of research was proposed ...

The Two Hyperplane Conjecture

作者：David; JERISON 刊期：2019年第06期

We introduce a conjecture that we call the Two Hyperplane Conjecture, saying that an isoperimetric surface that divides a convex body in half by volume is trapped between parallel hyperplanes. The conjecture is motivated by an approach we propose to the Hots Spots Conjecture of J. Rauch using deformation and Lipschit...

Perturbation Theory for Solutions to Second Order Elliptic Operators with Complex Coefficients and the L~p Dirichlet Problem

作者：Martin; DINDOS; Jill; PIPHER 刊期：2019年第06期

We establish a Dahlberg-type perturbation theorem for second order divergence form elliptic operators with complex coefficients. In our previous paper, we showed the following result: If L0 = div A0(x)■+ B0(x) · ■ is a p-elliptic operator satisfying the assumptions of Theorem 1.1 then the LpDirichlet problem for th...

Subsets of Euclidean Space with Nearly Maximal Gowers Norms

作者：Michael; CHRIST 刊期：2019年第06期

A set E ? R~d whose indicator function 1_E has maximal Gowers norm, among all sets of equal measure, is an ellipsoid up to Lebesgue null sets. If 1_E has nearly maximal Gowers norm then E nearly coincides with some ellipsoid, in the sense that their symmetric difference has small Lebesgue measure.

Near Equality in the Riesz–Sobolev Inequality

作者：Michael; CHRIST 刊期：2019年第06期

The Riesz–Sobolev inequality provides a sharp upper bound for a trilinear expression involving convolution of indicator functions of sets. Equality is known to hold only for indicator functions of appropriately situated intervals. We characterize ordered triples of subsets of R~1 that nearly realize equality, with q...

Nodal Sets and Doubling Conditions in Elliptic Homogenization

作者：Fanghua; Lin; Zhongwei; Shen 刊期：2019年第06期

This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients. We show that the(d-1)-dimensional Hausdorff measures of the nodal sets of ...

Accretivity of the General Second Order Linear Differential Operator

作者：V.G.MAZ’YA; I.E.VERBITSKY 刊期：2019年第06期

Hardy–Littlewood–Sobolev Inequalities with the Fractional Poisson Kernel and Their Applications in PDEs

作者：Lu; CHEN; Guozhen; LU; Chunxia; TAO 刊期：2019年第06期

A New Elliptic Measure on Lower Dimensional Sets

作者：Guy; DAVID; Joseph; FENEUIL; Svitlana; MAYBORODA 刊期：2019年第06期

The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of n-1 dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys the first steps of a program recently launched by the authors and aimed at the n...

Randomness and Nonlinear Evolution Equations

作者：Andrea; R.NAHMOD; Gigliola; STAFFILANI 刊期：2019年第06期

In this paper we survey some results on existence, and when possible also uniqueness, of solutions to certain evolution equations obtained by injecting randomness either on the set of initial data or as a perturbative term.

On the Global Regularity for a Wave-Klein–Gordon Coupled System

作者：Alexandru; D.IONESCU; Benoit; PAUSADER 刊期：2019年第06期

In this paper we consider a coupled Wave-Klein–Gordon system in 3 D, and prove global regularity and modified scattering for small and smooth initial data with suitable decay at infinity. This system was derived by Wang and LeFloch–Ma as a simplified model for the global nonlinear stability of the Minkowski space-t...

Transmission Eigenvalues and the Riemann Zeta Function in Scattering Theory for Automorphic Forms on Fuchsian Groups of Type Ⅰ

作者：Fioralba; CAKONI; Sagun; CHANILLO 刊期：2019年第06期

We introduce the concept of transmission eigenvalues in scattering theory for automorphic forms on fundamental domains generated by discrete groups acting on the hyperbolic upper half complex plane. In particular, we consider Fuchsian groups of Type Ⅰ. Transmission eigenvalues are related to those eigen-parameters f...

Quantitative Absolute Continuity of Harmonic Measure and the Dirichlet Problem: A Survey of Recent Progress

作者：Steve; HOFMANN 刊期：2019年第06期

Type Ⅱ Blow-up in the 5-dimensional Energy Critical Heat Equation

作者：Manuel; del; PINO; Monica; MUSSO; Jun; Cheng; WEI 刊期：2019年第06期

We consider the Cauchy problem for the energy critical heat equation ■ in dimension n = 5. More precisely we find that for given points q1, q2,..., qk and any sufficiently small T > 0 there is an initial condition u0 such that the solution u(x, t) of(0.1) blows-up at exactly those k points with rates type Ⅱ, namely...