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dirichlet PROBLEMS FOR MONGE-AMPERE EQUATION DEGENERATE ON BOUNDARY

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Chinese Annals of Mathematics,Series B 1991年第4期12卷 407-420页

作者：洪家兴 Institute of Mathematics Fudan University Shanghai China

The existence of C~∞ -solutions to dirichlet problem for Monge-Ampere equation degenerate on boundary is proved, and some applications to the equation prescribed Gaussian curvature are also given.

关键词： dirichlet degenerate curvature prescribed regularity argument tangent enough defining estimates

Extrapolation for the L^p dirichlet Problem in Lipschitz Domains

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Acta Mathematica Sinica,English Series 2019年第6期35卷 1074-1084页

作者： Zhongwei Shen Department of Mathematics University of Kentucky

Let L be a second-order linear elliptic operator with complex coefficients. It is shown that if the L^p dirichlet problem for the elliptic system L(u) = 0 in a fixed Lipschitz domain Ω in Rd is solvable for some 1 < p = p_0 <2(d-1)/(d-2), then it is solvable for all p satisfying ■ The proof is based on a real-variable argument. It only requires that local solutions of L(u) = 0 satisfy a boundary Cacciopoli inequality.

关键词： dirichlet problem Lipschitz domain extrapolation

On the dirichlet form of three-dimensional Brownian motion conditioned to hit the origin

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Science China Mathematics 2019年第8期62卷 1477-1492页

作者： Patrick J. Fitzsimmons Liping Li Department of Mathematics University of California at San Diego San Diego CA 92093-0112 USA RCSDS HCMS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China

Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to C_c^∞(R^3\{0}).We will prove that this energy form is a regular dirichlet form with core C_c^∞(R^3).The associated diffusion X behaves like a 3-dimensional Brownian motion with a mild radial drift when far from 0,subject to an ever-stronger push toward 0 near that *** particular,{0}is not a polar set with respect to *** diffusion X is rotation invariant,and admits a skew-product representation before hitting{0}:its radial part is a diffusion on(0,∞)and its angular part is a time-changed Brownian motion on the sphere S^*** radial part of X is a"reflected"extension of the radial part of X^0(the part process of X before hitting{0}).Moreover,X is the unique reflecting extension of X^0,but X is not a semi-martingale.

关键词： dirichlet form reflected extension rotationally invariant process Fukushima’s decomposition

RADIAL CONVEX SOLUTIONS OF A SINGULAR dirichlet PROBLEM WITH THE MEAN CURVATURE OPERATOR IN MINKOWSKI SPACE

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Acta Mathematica Scientia 2019年第2期39卷 395-402页

作者： Zaitao LIANG 杨艳娟 School of Mathematics and Big Data Anhui University of Science and Technology College of Sciences Hohai University

In this paper, we study the existence of nontrivial radial convex solutions of a singular dirichlet problem involving the mean curvature operator in Minkowski space. The proof is based on a well-known fixed point theo... 详细信息

关键词： radial convex solutions singular dirichlet problem mean curvature operator fixed point theorem in cones

Properties of Toeplitz Operators on the dirichlet Space Over the Ball

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Acta Mathematica Sinica,English Series 2019年第10期35卷 1617-1628页

作者： Yin Yin HU Yu Feng LU Liu LIU Department of Mathematics Dalian Maritime UniversityDalian 116024P.R.China Department of Mathematics Dalian University of TechnologyDalian 116024P.R.China

On the dirichlet space of the unit ball, we study some algebraic properties of Toeplitz operators. We give a relation between Toeplitz operators on the dirichlet space and their analogues defined on the Hardy space. Based on this, we characterize when finite sums of products of Toeplitz operators are of finite rank. Also, we give a necessary and sufficient condition for the commutator and semi-commutator of two Toeplitz operators being zero.

关键词： Toeplitz operator pluriharmonic symbols dirichlet space

THE VALUE DISTRIBUTION OF RANDOM ANALYTIC dirichlet SERIES OF NEUTRAL GROWTH(I)

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Acta Mathematica Scientia 1999年第2期19卷 234-240页

作者：丁晓庆 Wuhan Univ Dept Math Wuhan 430072 Peoples R China

This paper deals with the value distribution of random dirichlet series whose coefficients are a martingale difference sequence, and which is of neutral growth.

关键词： Value distribution random dirichlet series martingale difference sequence.

Dual variational formulas for the first dirichlet eigenvalue on half-line

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Science China Mathematics 2003年第6期46卷 847-861页

作者：陈木法张余辉赵晓亮 Beijing Normal University Beijing 100875 China

The aim of the paper is to establish two dual variational formulas for the first dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied.

关键词： first dirichlet eigenvalue, variational formula, elliptic operator, birth-death process.

Multipliers on dirichlet Type Spaces

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Acta Mathematica Sinica,English Series 2001年第2期17卷 263-272页

作者： Peng Yan HU Department of Mathematics. Normal College of Shenzhen University. Shenzhen. Guangdong 518060. P. R. China Ji Huai SHI Department of Mathematics. University of Science and Technology of China. Hefei. Anhui 230026, P. R. China Department of Mathematics Normal College of Shenzhen University Shenzhen Guangdong 518060 P. R. China Department of Mathematics University of Science and Technology of China Hefei Anhui 230026 P. R. China

In this paper, we characterize the pointwise multiplier space M(D_τ, D_μ) of dirichlet type spaces in the unit ball of C^n for the values of τ, μ in three cases: (i)τn. and construct two functions to show that M... 详细信息

关键词： dirichlet space Pointwise multiplier Holomorphic function

Interior gradient and Hessian estimates for the dirichlet problem of semi-linear degenerate elliptic systems: A probabilistic approach

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Science China Mathematics 2019年第10期62卷 1851-1886页

作者： Jun Dai Shanjian Tang Bingjie Wu School of Mathematical Sciences Fudan University

In this paper, we give interior gradient and Hessian estimates for systems of semi-linear degenerate elliptic partial differential equations on bounded domains, using both tools of backward stochastic differential equ... 详细信息

关键词： semi-linear degenerate elliptic systems quasi-derivatives backward stochastic differential equations dirichlet problems