检索结果-南通市图书馆

C^(α)regularity of weak solutions of non-homogeneous ultraparabolic equations with drift terms

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2024年第1期67卷 23-44页

作者： Wendong Wang Liqun Zhang School of Mathematical Sciences Dalian University of TechnologyDalian 116024China Institute of Mathematics Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

We consider a class of non-homogeneous ultraparabolic differential equations with singular drift terms arising from some physical models,and prove that weak solutions are H?lder continuous,which are sharp in some sense and also generalize the well-known De Giorgi-Nash-Moser theory to degenerate parabolic equations satisfying the H?rmander hypoellipticity *** new ingredients are manifested in two aspects:on the one hand,for lower-order terms,we exploit a new Sobolev inequality suitable for the Moser iteration by improving the result of Pascucci and Polidoro(2004);on the other hand,we explore the G-function from an early idea of Kruzhkov(1964)and an approximate weak Poincaréinequality for non-negative weak sub-solutions to prove the H?lder regularity.

关键词： ultraparabolic equations Moser iteration poincare inequality C^a regularity

Variational Formulas of poincare-Type Inequalities in Banach Spaces of Functions on the Line

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2002年第3期18卷 417-436页

作者： Mu Fa CHEN Department of Mathematics. Beijing Normal. University. Beijing 100875. P. R. China Department of Mathematics Beijing Normal University Beijing P. R. China

Motivated from the study on logarithmic Sobolev. Nash and other functional inequalities, the variational formulas for poincare inequalities are extended to a large class of Banach (Orlicz) spaces of functions on the line. Explicit criteria for the inequalities to hold and explicit estimates for the optimal constants in the inequalities are presented. As a typical application, the logarithmic Sobolev constant is carefully examined.

关键词： Variational formula poincare inequality Logarithmic Sobolev inequality Orliez space

Poincar and Weak Poincar Inequalities for the Mixed Poisson Measure

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2014年第10期30卷 1719-1728页

作者： Chang Song DENG School of Mathematics and Statistics Wuhan University

By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both poincare and weak poincare inequalities are established, while another poincare type in... 详细信息

关键词： Mixed Poisson measure poincare inequality configuration space birth-death process

Variational Formulas of Poincaré-type Inequalities for Birth-Death Processes

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2003年第4期19卷 625-644页

作者： MuFaCHEN DepartmentofMathematics BeijingNormalUniversityBeijing100875P.R.China

In author's one previous paper, the same topic was studied for onedimensional diffusions. As a continuation, this paper studies the discrete case, that is thebirth-death processes. The explicit criteria for the inequalities, the variational formulas andexplicit bounds of the corresponding constants in the inequalities are presented. As typicalapplications, the Nash inequalities and logarithmic Sobolev inequalities are examined.

关键词： variational formula poincare inequality Nash inequality logarithmicSobolev inequality orlicz space birth-death process

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

RCD（K,N）空间上的调和函数

RCD（K,N）空间上的调和函数

作者：孙禄康南京大学

学位级别：硕士

Lott,Sturm和Villani给出了度量测度空间Ricci曲率下界的定义,之后Ambrosio,Gigli和Savare又将Jordan,Kinderlehrer和Otto的欧式空间上熵流与热流的等价性结果推广到RCD(K,∞)空间(K∈R)上,RCD(K,∞)空间(K∈R)包含RCD(K,N)空间(K≥0,N∈[1,∞))。在RCD(K,N)空间(K≥0,N∈[1,∞))上可以应用狄氏型(Dirichlet form)理论给出Laplace算子的定义,本文主要利用Moser迭代技巧建立RCD(K,N)空间(K≥0,N∈[1,∞))上调和函数的一系列性质,包括对应调和函数的Harnack不等式,Holder连续性及满足多项式增长的调和函数组成的函数空间的维数有上界。本文还利用半群方法证明RCD(K,N)空间(K>0,N∈[1,∞))上不存在非常数的调和函数及RCD(K,N)空间(K≥0,N∈[1,∞))上调和函数的Liouville定理。

关键词： RCD(K,N)Space Laplacian Liouville Theorem Sobolev embedding poincare inequality Ricci Curvature Optimal Transport Curvature Dimension condition