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Viscosity Solutions to a Parabolic Inhomogeneous Equation Associated with Infinity Laplacian

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Acta Mathematica Sinica,English Series 2015年第2期31卷 255-271页

作者： Fang LIU xiao ping yang Department of Applied Mathematics School of Science Nanjing University of Science & Technology

We obtain the existence and uniqueness results of viscosity solutions to the initial and boundary value problem for a nonlinear degenerate and singular parabolic inhomogeneous equation of the form ut-△ ∞N u=f, wher... 详细信息

关键词： Parabolic equation infinity Laplacian viscosity solution inhomogeneous equation comparison principle existence

Viscosity Analysis on the Boltzmann Equation

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Acta Mathematica Sinica,English Series 2012年第10期28卷 2139-2152页

作者： Min Ling ZHENG xiao ping yang School of Science Huzhou Teachers College School of Science Nanjing University of Science&Technology

This paper is devoted to investigating the asymptotic properties of the renormalized so- lution to the viscosity equation δtfε ＋ v · △↓xfε = Q（fε, fε）＋ ε△vfε as ε →0＋. We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L^1（（0, T） × RN × R^N）. The proof is based on compactness analysis and velocity averaging theory.

关键词： Viscosity Boltzmann equation renormalized solution viscosity coemcient defect measure

An Analysis of Two Variational Models for Speckle Reduction of Ultrasound Images

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Acta Mathematicae Applicatae Sinica 2016年第4期32卷 969-982页

作者： Zheng-meng JIN xiao-ping yang School of Science Nanjing University of Posts and Telecommunications School of Science Nanjing University of Science and Technology

In this paper, we consider two variational models for speckle reduction of ultrasound images. By employing the F-convergence argument we show that the solution of the SO model coincides with the minimizer of the JY model. Furthermore, we incorporate the split Bregman technique to propose a fast alterative algorithm to solve the JY model. Some numericalexperiments are presented to illustrate the efficiency of the proposed algorithm.

关键词： BV F-convergence equivalence multiplicative noise Split Bregman algorithm

Analysis of a Hyperbolic-Parabolic Type System for Image Inpainting

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Acta Mathematica Sinica,English Series 2012年第8期28卷 1663-1676页

作者： Zheng Meng JIN xiao ping yang School of Science Nanjing University of Posts and Telecommunications School of Science Nanjing University of Science and Technology

In this paper we consider the initial boundary value problem of a hyperbolic-parabolic type system for image inpainting in a 2-D bounded domain, and establish the existence of weak solutions to the system by employing... 详细信息

关键词： Weak solutions hyperbolic-parabolic type system vanishing viscosity image inpainting

Some Properties of Abnormal Extremals on Lie Groups

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Acta Mathematica Sinica,English Series 2014年第12期30卷 2119-2136页

作者： Ti Ren HUANG xiao ping yang Department of Mathematics Zhejiang Sci-Tech University Department of Applied Mathematics Nanjing University of Science & Technology

Let G be a connected Lie group and D be a bracket generating left invariant *** this paper,first,we prove that all sub-Riemannian minimizers are smooth in Lie groups if the distribution D satisfies [D,[D,D]]D and [K,[K,K]]K for any proper sub-distribution K of ***,we prove that all sub-Riemannian minimizers are smooth in Lie group if the rank-3 distribution D satisfies Condition（B）.Third,we discuss characterizations of normal extremals,abnormal extremals,rigid curves,and minimizers on product sub-riemannian Lie *** prove that not all strictly abnormal minimizers are rigid curves and construct a strictly abnormal minimizer which is not a rigid curve.

关键词： Extremal geodesic rigid curve Lie group

Horizontal Connection and Horizontal Mean Curvature in Carnot Groups

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Acta Mathematica Sinica,English Series 2006年第3期22卷 701-710页

作者： Kang Hai TAN xiao ping yang Department of Applied Mathematics Nanjing University of Science and Technology

In this paper we give a geometric interpretation of the notion of the horizontal mean curvature which is introduced by Danielli Garofalo-Nhieu and Pauls who recently introduced sub- Riemannian minimal surfaces in Carnot groups. This will be done by introducing a natural nonholonomic connection which is the restriction （projection） of the natural Riemannian connection on the horizontal bundle. For this nonholonomic connection and （intrinsic） regular hypersurfaces we introduce the notions of the horizontal second fundamental form and the horizontal shape operator. It turns out that the horizontal mean curvature is the trace of the horizontal shape operator.

关键词： Carnot groups Nonholonomic connection Horizontal mean curvature Sub-Riemannian minimal surfaces

The Upper Bounds of Arbitrary Eigenvalues for Uniformly Elliptic Operators with Higher Orders

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Acta Mathematicae Applicatae Sinica 2006年第4期22卷 589-598页

作者： Gao Jia xiao-ping yang College of Science University of Shanghai for Science and Technology Shanghai 200093 China School of Science Nanjing University of Science and Technology Nanjing 210094 China

Let Ωbelong to R^m （m≥ 2） be a bounded domain with piecewise smooth and Lipschitz boundary δΩ Let t and r be two nonnegative integers with t ≥ r ＋ 1. In this paper, we consider the variable-coefficient eigenvalue problems with uniformly elliptic differential operators on the left-hand side and （-Δ）^T on the right-hand side. Some upper bounds of the arbitrary eigenvalue are obtained, and several known results are generalized.

关键词： Uniformly elliptic operator of any order eigeuvalue eigenfunction upper bound

A Lower Semicontinuity Result for Some Integral Functionals in the Space SBD

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Acta Mathematicae Applicatae Sinica 2008年第2期24卷 297-304页

作者： Zhong-xue Lu xiao-ping yang Min-ling Zheng School of Mathematical Science Xuzhou Normal University Xuzhou 221116 China School of Science Nanjing University of Science and Technology Nanjing 210094 China School of Science Huzhou Teacher College Huzhou 313000 China

In this paper, we obtain a lower semicontinuity result with respect to the strong L1-convergence of the integral functionals F（u,Ω）=Ωf（x,u（x）,εu（x））dx defined in the space SBD of special functions with bounded deformation. Here Su represents the absolutely continuous part of the symmetrized distributional derivative Eu. The integrand f satisfies the standard growth assumptions of order p 〉 1 and some other conditions. Finally, by using this result,we discuss the existence of an constrained variational problem.

关键词： SBD space integral functionals lower semicontinuity

Some Properties of Quasiconvex Functions on the Heisenberg Group

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Acta Mathematicae Applicatae Sinica 2005年第4期21卷 571-580页

作者： Ming-bao Sun xiao-ping yang Department of Applied Mathematics Hunan Institute of Science and Technology Yueyang 414000 China Department of Applied Mathematics Nanjing University of Science and Technology Nanjing 210094 China

For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L^∞ norm of the first derivatives of h-quasiconvex functions.

关键词： h-quasiconvex function h-convex function Heisenberg group