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Subelliptic Harmonic Maps with Values in Metric Spaces of Nonpositive Curvature

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Communications in Mathematical Research 2022年第4期38卷 516-534页

作者： Yaoting Gui Jürgen Jost Xianqing Li-Jost School of Mathematical Sciences University of Science and Technology of ChinaHefeiChina Max Planck Institute for Mathematics in the Sciences LeipzigGermany

We prove the holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with nonpositive curvature,and more generally into a non-positively curved metric space in th... 详细信息

关键词： Subelliptic harmonic maps nonpositive curvature holder continuity

ON THE NECESSARY AND SUFFICIENT CONDITIONS TO SOLVE A HEAT EQUATION WITH GENERAL ADDITIVE GAUSSIAN NOISE

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Acta Mathematica Scientia 2019年第3期39卷 669-690页

作者： Yaozhong HU Yanghui LIU Department of Mathematical and Statistical Sciences University of AlbertaEdmontonT6G 2G1Canada Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA

In this note, we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two differen t met hods, respectively, based on variance compu tations and on pat h-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.

关键词： Stochastic heat equation general Gaussian noise L^(2) solution sufficient and necessary condition Wong-Zakai approximation pathwise solution holder continuity Besov space

ON THE continuity AND DIFFERENTIABILITY OF AKIND OF FRACTAL INTERPOLATION FUNCTION

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Applied Mathematics and Mechanics(English Edition) 2002年第4期23卷 471-478页

作者：李红达叶正麟高行山 State Key Laboratory of Information Security Graduate School C hinese Academy of Sciences Beijing 100039 P R China Department of Mathematics and Information Northwestern Polytechnical University Xi'an 710072 P R China Department of Engineering Mechanics Northwestern Polytechnical University Xi'an 710072 P R China

The sufficient conditions of holder continuity of two kinds of fractal interpolation functions defined by IFS (Iterated Function System) were obtained. The sufficient and necessary condition for its differentiability was proved. Its derivative was a fractal interpolation function generated by the associated IFS, if it is differentiable.

关键词： fractal interpolation function holder continuity differentiability

Stochastic Fractional Anderson Models with Fractional Noises

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 101-118页

作者： Yiming JIANG Kehua SHI Yongjin WANG School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China School of Mathematical Sciences and LPMC Nankai University Tianjin 300071 China

The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its HSlder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.

关键词： Anderson models Fractional noises Lyapunov exponent holder continuity Absolute continuity

SOME RECENT PROGRESS ON STOCHASTIC HEAT EQUATIONS

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Acta Mathematica Scientia 2019年第3期39卷 874-914页

作者： Yaozhong HU Department of Mathematical and Statistical Sciences University of Alberta

This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.

关键词： Gaussian random field Gaussian noise stochastic partial differential equation(stochastic heat equation) Feynman-Kac formula for the solution FeynmanKac formula for the moments of the solution chaos expansion hypercontractivity moment bounds holder continuity joint holder continuity asymptotic behaviour Trotter-Lie formula Skorohod integral

Construction and Dimension Analysis for a Class of Fractal Functions

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Acta Mathematicae Applicatae Sinica 2002年第3期18卷 431-440页

作者： Hong-yong Wang, Zong-ben XuDepartment of Mathematics, Huaibei Coal Industry Teachers College, Huaibei 235000, ChinaResearch Center for Applied Mathematics, Faculty of Science, Xi’an Jiaotong University, Xi’an 710049, China Department of Mathematics Huaibei Coal Industry Teachers College Huaibei China Research Center for Applied Mathematics Faculty of Sciences Xi'an Jiaotong University Xi'an China

In this paper, we construct a class of nowhere differentiable continuous functions by means of the Cantor series expression of real numbers. The constructed functions include some known nondifferentiable functions, such as Bush type functions. These functions are fractal functions since their graphs are in general fractal sets. Under certain conditions, we investigate the fractal dimensions of the graphs of these functions, compute the precise values of Box and Packing dimensions, and evaluate the Hausdorff dimension. Meanwhile, the holder continuity of such functions is also discussed.

关键词： Cantor series expression dyadic nondifferentiable fractal dimension holder continuity

Remarks on the Harnak Inequality for Local-Minima of Scalar Integral Functionals with General Growth Conditions

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Journal of Applied Mathematics and Physics 2014年第5期2卷 194-203页

作者： Tiziano Granucci Scuola Superiore Istituto P.CalamandreiFirenzeItaly

In this paper we proof a Harnack inequality and a regularity theorem for local-minima of scalar intagral functionals with general growth conditions.

关键词： Harnack Inequality Regularity holder continuity

holder Regularity for Abstract Fractional Cauchy Problems with Order in(0,1)

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Journal of Applied Mathematics and Physics 2018年第1期6卷 310-319页

作者： Chenyu Li Miao Li Department of Mathematics Sichuan University Chengdu China

In this paper, we study the regularity of mild solution for the following fractional abstract Cauchy problem Dt αu(t)=Au(t)+f(t), t ∈ (0,T] u(0)= x0 on a Banach space X with order α ∈ (0,1), where the fractional derivative is understood in the sense of Caputo fractional derivatives. We show that if A generates an analytic α-times resolvent family on X and f ∈ Lp ([0,T];X) for some p > 1/α, then the mild solution to the above equation is in Cα-1/p[ò,T] for every ò > 0. Moreover, if f is H?lder continuous, then so are the Dt αu(t) and Au(t).

关键词： Fractional Cauchy Problem Fractional Resolvent Family Generator Regularity holder continuity

A Class of Fractal Functions and Their Dimension Estimates

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Chinese Quarterly Journal of Mathematics 2000年第4期15卷 84-90页

作者：王宏勇杨守志西安交通大学理学院淮北煤炭师范学院数学系

本文作者首先借助于b进制分数及无穷级数构造了一类分形函数，然后研究了这些函数图象的分形维数及其Hoelder性质，得到了一些维数结果。

关键词： b-adic fraction fractal function fractal dimension holder continuity