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Regularity for anisotropic solutions to some nonlinear elliptic system

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Frontiers of Mathematics in China 2016年第1期11卷 77-87页

作者： hongya gao Shuang LIANG Yi CUI College of Mathematics and Information Science Hebei University Baoding 071002 China

Abstract This paper deals with anisotropic solutions u∈W1,（pi）（Ω,RN）to-n∑i=1Di（aα/i（x,Du（x）））=-n∑i=1DiFα/i（x）,α=1,2...,N.We present a rnonotonicity inequality for the matrix a=（aα/i）∈Rn×n,which... 详细信息

关键词： Regularity anisotropic solution nonlinear elliptic system

Global Integrability for Solutions to Obstacle Problems

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Journal of Partial Differential Equations 2022年第4期35卷 320-330页

作者： SHAN Yanan gao hongya Hebei Key Laboratory of Machine Learning and Computational Intelligence College of Mathematics and Information ScienceHebei UniversityBaoding 071002China

DenoteκψØ(Ω)={υ∈w1,p(Ω):υ≥ψ,a,e.andυ-Ø∈w1,po(Ω)},where is any function in Q C R^(N),N≥2,with values in RU[±∞]and e is a measurable function.This paper deals with global integrability for u E Kμ,e such ... 详细信息

关键词： Global integrability obstacle problem A-harmonic equation

An Optimal Inequality for One-Parameter Mean

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Journal of Applied Mathematics and Physics 2013年第5期1卷 45-48页

作者： hongya gao Yanjie Zhang Tian Wang College of Mathematics and Computer Science Hebei University Baoding China

In the present paper, we answer the question: for 0 what are the greatest value p(a) and the least value q(a) such that the inequality. For more information about abstract,please download the PDF file.

关键词： Optimal Inequality One-Parameter Mean Arithmetic Mean Geometric Mean

An Optimal Double Inequality among the One-Parameter, Arithmetic and Geometric Means

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Journal of Applied Mathematics and Physics 2013年第7期1卷 1-4页

作者： hongya gao Shuangli Li Yanjie Zhang Hong Tian College of Mathematics and Computer Science Hebei University Baoding China

In the present paper, we answer the question: for 0a what are the greatest value p(a) and the least value q(a) such that the double inequality Jp(a,b)aA(a,b)+ (1-a)G(a,b)Jq(a,b) holds for all a,b>0 with a is not equal... 详细信息

关键词： Optimal Double Inequality One-Parameter Mean Arithmetic Mean Geometric Mean

Regularity for solutions to anisotropic obstacle problems

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Science China Mathematics 2014年第1期57卷 111-122页

作者： gao hongya College of Mathematics and Computer Science Hebei University

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.***.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.

关键词： local regularity,local boundedness,anisotropic obstacle problem,A-harmonic equation,integral functional

Integrability for the Jacobian of orientation-preserving forms

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Science China Mathematics 2005年第11期48卷 1488-1498页

作者： gao hongya ZHAO Hongliang College of Mathematics and Computer Science Hebei University Baoding 071002 China Department of Mathematics and Physics Qingdao Institute of Architecture and Engineering Qingdao 266033 China

This paper considers the integrability for the Jacobian of orientation-preserving forms in anisotropic Sobolev classes. The main result is a sufficient condition ensuring integrability of the Jacobian, which can be re... 详细信息

关键词： Jacobian,integrability,Hadamard's inequality,Hodge decomposition

REGULARITY FOR VERY WEAK SOLUTIONS TO A-HARMONIC EQUATION

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Applied Mathematics(A Journal of Chinese Universities) 2006年第3期21卷 343-349页

作者： Liu Lin gao hongya Applied Science School University of Science and Technology Beijing Beijing 100083China. College of Mathematics and Computer Science Hebei University Baoding 071002 China.

In this paper, the following result is given by using Hodge decomposition and weak reverse Holder inequality： For every r1 with P-（2^n＋1 100^n^2 p（2^3＋n/（P-1）＋1）b/a）^-1〈r1〈p,there exists the exponent r2 = r2（n, r1,p）〉 p, such that for every very weak solution u∈W^1r1,loc（Ω） to A-harmonic equation, u also belongs to W^1r2,loc（Ω） . In particular, u is the weak solution to A-harmonic equation in the usual sense.

关键词： A-harmonic equation very weak solution Hodge decomposition weak reverse Holder inequality.

TWO GENERALIZATIONS OF HARDY-LITTLEWOOD MAXIMAL OPERATOR

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Applied Mathematics(A Journal of Chinese Universities) 2006年第1期21卷 59-63页

作者： gao hongya Zhao Hongliang College of Mathematics and Computer Science Hebei University Baoding 071002China Department of Mathematics Qingdao Institute of Architecture and EngneeringQingdao 266033China.

Two generalizations of Hardy-Littlewood maximal operator are considered. Some estimates for them are obtained.

关键词： Hardy-Littlewood maximal operator weak maximal operator spherical average Morrey type operator,outer Hausdorff measure.

Size and elemental composition of dry-deposited particles during a severe dust storm at a coastal site of Eastern China

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Journal of Environmental Sciences 2016年第2期28卷 161-168页

作者： hongya Niu Daizhou Zhang Wei Hu Jinhui Shi Ruipeng Li Huiwang gao Wei Pian Min Hu State Key Joint Laboratory of Environmental Simulation and Pollution Control College of Environmental Sciences and EngineeringPeking University Hebei Collaborative Innovation Center of Coal Exploitation Hebei University of Engineering Faculty of Environmental and Symbiotic Sciences Prefectural University of Kumamoto Key Laboratory of Marine Environmental Science and Ecology Ocean University of ChinaMinistry of Education

Dry-deposited particles were collected during the passage of an extremely strong dust storm in March, 2010 at a coastal site in Qingdao（36.15°N, 120.49°E）, a city located in Eastern China. The size, morphology, and elemental composition of the particles were quantified with a scanning electron microscope equipped with an energy dispersive X-ray instrument（SEM–EDX）. The particles appeared in various shapes, and their size mainly varied from 0.4to 10 μm, with the mean diameters of 0.5, 1.5, and 1.0 μm before, during, and after the dust storm, respectively. The critical size of the mineral particles settling on the surface in the current case was about 0.3–0.4 μm before the dust storm and about 0.5–0.7 μm during the dust storm. Particles that appeared in high concentration but were smaller than the critical size deposited onto the surface at a small number flux. The elements Al, Si and Mg were frequently detected in all samples, indicating the dominance of mineral particles. The frequency of Al in particles collected before the dust storm was significantly lower than for those collected during and after the dust storm. The frequencies of Cl and Fe did not show obvious changes, while those of S, K and Ca decreased after the dust arrival. These results indicate that the dust particles deposited onto the surface were less influenced by anthropogenic pollutants in terms of particle number.

关键词： Asian dust Dry deposition Morphology Size distribution Elemental composition