Lin, Fanghua
Overview
Works:  38 works in 106 publications in 3 languages and 1,758 library holdings 

Genres:  Textbooks Conference papers and proceedings 
Roles:  Author, Editor 
Classifications:  QA377, 515.353 
Publication Timeline
.
Most widely held works by
Fanghua Lin
Elliptic partial differential equations by
Qing Han(
Book
)
26 editions published between 1997 and 2011 in English and held by 336 WorldCat member libraries worldwide
26 editions published between 1997 and 2011 in English and held by 336 WorldCat member libraries worldwide
The analysis of harmonic maps and their heat flows by
Fanghua Lin(
Book
)
14 editions published in 2008 in English and Undetermined and held by 156 WorldCat member libraries worldwide
"This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis."Jacket
14 editions published in 2008 in English and Undetermined and held by 156 WorldCat member libraries worldwide
"This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis."Jacket
Geometric measure theory : an introduction by
Fanghua Lin(
Book
)
11 editions published between 2002 and 2010 in English and Spanish and held by 86 WorldCat member libraries worldwide
11 editions published between 2002 and 2010 in English and Spanish and held by 86 WorldCat member libraries worldwide
Lectures on the analysis of nonlinear partial differential equations(
Book
)
8 editions published between 2012 and 2013 in English and held by 25 WorldCat member libraries worldwide
8 editions published between 2012 and 2013 in English and held by 25 WorldCat member libraries worldwide
Nonlinear partial differential equations : proceedings of International Conference, Zhejiang University, June 1992(
Book
)
4 editions published in 1993 in English and held by 13 WorldCat member libraries worldwide
4 editions published in 1993 in English and held by 13 WorldCat member libraries worldwide
On the wellposedness of boundary layer equations by Tak Kwong Wong(
)
1 edition published in 2010 in English and held by 7 WorldCat member libraries worldwide
In this thesis we are concerned with partial differential equations arising from boundary layer problems, namely, hydrostatic Euler equations and Prandtl equations. After a brief survey of the current progress of the hydrostatic Euler equations, we establish the local existence and uniqueness of Hs solutions under the local Rayleigh condition. The proof is based on new weighted Hs estimates. Moreover, we provide a finite time blowup result as well. For the Prandtl equations, we first give a brief introduction of the known existence and illposedness results. Then, under Oleinik's monotonicity assumption, we prove the local existence of weak solutions to the Prandtl equations by the viscoussplitting algorithm
1 edition published in 2010 in English and held by 7 WorldCat member libraries worldwide
In this thesis we are concerned with partial differential equations arising from boundary layer problems, namely, hydrostatic Euler equations and Prandtl equations. After a brief survey of the current progress of the hydrostatic Euler equations, we establish the local existence and uniqueness of Hs solutions under the local Rayleigh condition. The proof is based on new weighted Hs estimates. Moreover, we provide a finite time blowup result as well. For the Prandtl equations, we first give a brief introduction of the known existence and illposedness results. Then, under Oleinik's monotonicity assumption, we prove the local existence of weak solutions to the Prandtl equations by the viscoussplitting algorithm
The lattice Faddeev Model by Hans K Shmidheiser(
)
2 editions published in 2009 in English and held by 7 WorldCat member libraries worldwide
We describe a lattice version of the Faddeev Model for knotted solitons. We briefly mention the known results for the original Faddeev Model, including the 3/4energy growth law and the existence results of Lin and Yang. Then we discuss numerical implementations of the model by Faddeev, Battye and Sutcliffe and Ward, motivating the theoretical study of the Lattice Faddeev Model. In particular, we will focus on how one computes a Hopf number for a nice map from R3 to S2 by sampling at integer lattice points Z3. Alternatively, we discuss how one can use this to assign Hopf numbers to a map from Z3 to S2. We then describe how this technique could be generalized to compute general topological invariants for maps between manifolds, given in terms of differential forms, by sampling at a discrete set of points. We characterize some of the function spaces involved in the Lattice Faddeev Model, and derive some energy estimates. Finally, we apply the techniques of Lin and Yang to the Lattice Faddeev Model, to obtain existence results
2 editions published in 2009 in English and held by 7 WorldCat member libraries worldwide
We describe a lattice version of the Faddeev Model for knotted solitons. We briefly mention the known results for the original Faddeev Model, including the 3/4energy growth law and the existence results of Lin and Yang. Then we discuss numerical implementations of the model by Faddeev, Battye and Sutcliffe and Ward, motivating the theoretical study of the Lattice Faddeev Model. In particular, we will focus on how one computes a Hopf number for a nice map from R3 to S2 by sampling at integer lattice points Z3. Alternatively, we discuss how one can use this to assign Hopf numbers to a map from Z3 to S2. We then describe how this technique could be generalized to compute general topological invariants for maps between manifolds, given in terms of differential forms, by sampling at a discrete set of points. We characterize some of the function spaces involved in the Lattice Faddeev Model, and derive some energy estimates. Finally, we apply the techniques of Lin and Yang to the Lattice Faddeev Model, to obtain existence results
Universal symplectic forms in the soliton theory by Fedor Soloviev(
)
1 edition published in 2010 in English and held by 7 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
1 edition published in 2010 in English and held by 7 WorldCat member libraries worldwide
Using KricheverPhong's universal formula, we show that a multiplicative representation linearizes Sklyanian quadratic brackets for a multipole Lax function with a spectral parameter. The spectral parameter can be either rational or elliptic. As a byproduct, we obtain an extension of a Sklyanin algebra in the elliptic case. We discuss applications of these results to isospectral and isomonodromic equations with discrete time. KricheverPhong's formula provides a hierarchy of symplectic structures, and we show that there exists a nontrivial cubic bracket in Sklyanin's case. Also, we consider a generalization of the universal formula to variable base curves (suggested in [22]) in the simplest possible case of a rational base curve with moving marked points
Regularity of the free boundary of American options by Youngseok Lee(
)
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
We introduce pricing of American options on several assets that follow a geometric Brownian motion as a free boundary problem. A crucial assumption is that payoff functions are smooth in the region where the option is exercised. This assumption is true for various options traded in the derivatives market. A key ingredient for analysis of the free boundary is a monotonicity formula. Existence and uniqueness of homogeneous blowup limits at a fixed point on the free boundary are guaranteed by the monotonicity formula. Then the free boundary can be classified into high energy points and low energy points by nondegeneracy of the solution. The time projection of the set of high energy point is analyzed measure theoretically. We prove that the set of low energy points is locally spacetime C1,alpha. Finally, we can obtain C1,alpha regularity of the free boundary for some particular payoff functions
1 edition published in 2011 in English and held by 6 WorldCat member libraries worldwide
We introduce pricing of American options on several assets that follow a geometric Brownian motion as a free boundary problem. A crucial assumption is that payoff functions are smooth in the region where the option is exercised. This assumption is true for various options traded in the derivatives market. A key ingredient for analysis of the free boundary is a monotonicity formula. Existence and uniqueness of homogeneous blowup limits at a fixed point on the free boundary are guaranteed by the monotonicity formula. Then the free boundary can be classified into high energy points and low energy points by nondegeneracy of the solution. The time projection of the set of high energy point is analyzed measure theoretically. We prove that the set of low energy points is locally spacetime C1,alpha. Finally, we can obtain C1,alpha regularity of the free boundary for some particular payoff functions
Mappings minimizing the Lp norm of the gradient by
R Hardt(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Regularity at infinity for areaminimizing hypersurfaces in hyperbolic space by
R Hardt(
Book
)
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 3 WorldCat member libraries worldwide
Estimates for surfaces which are stationary for an elliptic parametric integral by
Fanghua Lin(
Book
)
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
Fei xian xing pian wei fen fang cheng fen xi jiang yi(
Book
)
2 editions published in 2013 in Chinese and English and held by 2 WorldCat member libraries worldwide
Ben shu shou ji le 8 pian jiang yi, bao guaNicolas Burqjiao shou deng guan yu shui bo wen tiCauchyli lun de di zheng ze xing, JeanYves Cheminjiao shou guan yuNavierStokesfang cheng, yi jiIsabelle Gallagherjiao shou guan yu hai yang liu de ban jing dian fen xi de jing cai nei rong deng
2 editions published in 2013 in Chinese and English and held by 2 WorldCat member libraries worldwide
Ben shu shou ji le 8 pian jiang yi, bao guaNicolas Burqjiao shou deng guan yu shui bo wen tiCauchyli lun de di zheng ze xing, JeanYves Cheminjiao shou guan yuNavierStokesfang cheng, yi jiIsabelle Gallagherjiao shou guan yu hai yang liu de ban jing dian fen xi de jing cai nei rong deng
Nonminimality of minimal graphs by
R Hardt(
Book
)
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1986 in English and held by 2 WorldCat member libraries worldwide
Rong ru shi cheng : Xinjiapo Futsing hui guan qian xi da qing te kan by
Xinjiapo Fuqing hui guan(
Book
)
1 edition published in 2000 in Chinese and held by 2 WorldCat member libraries worldwide
1 edition published in 2000 in Chinese and held by 2 WorldCat member libraries worldwide
On the NavierStokes equations by Hantaek Bae(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
This paper consists of two parts. The first part is the harmonic analysis methods for partial differential equations. We introduce the LittlewoodPaley decomposition, paradifferential calculus, and its application to the NavierStokes equations. Using the same idea, we prove that the dissipative quasigeostrophic equations are globally wellposedness in critical spaces
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
This paper consists of two parts. The first part is the harmonic analysis methods for partial differential equations. We introduce the LittlewoodPaley decomposition, paradifferential calculus, and its application to the NavierStokes equations. Using the same idea, we prove that the dissipative quasigeostrophic equations are globally wellposedness in critical spaces
Analysis of several sharpinterface limits in variational problems by Nam Quang Le(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
The third result addresses convergence results for critical points of the onedimensional AmbrosioTortorelli functional with fidelity term to those of the corresponding MumfordShah functional
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
The third result addresses convergence results for critical points of the onedimensional AmbrosioTortorelli functional with fidelity term to those of the corresponding MumfordShah functional
Lorentz space estimates and applied boundary current dynamics for GinzburgLandau by Ian Tice(
Book
)
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
This thesis, which is divided into three parts, is concerned with the study of the GinzburgLandau energy functional in two dimensions. In the first part, we prove novel lower bounds for the GinzburgLandau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results
1 edition published in 2008 in English and held by 1 WorldCat member library worldwide
This thesis, which is divided into three parts, is concerned with the study of the GinzburgLandau energy functional in two dimensions. In the first part, we prove novel lower bounds for the GinzburgLandau energy with or without magnetic field. These bounds rely on an improvement of the "vortex balls construction" estimates by extracting a new positive term in the energy lower bounds. This extra term can be conveniently estimated through a Lorentz space norm, on which it thus provides an upper bound. The Lorentz space we use is critical with respect to the expected vortex profiles and can serve to estimate the total number of vortices and get improved convergence results
On the Boltzmann equation: Hydrodynamic limit with longrange interactions and mild solutions by Diogo Arsenio(
Book
)
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
This thesis is devoted to the mathematical study of the Boltzmann equation, a fundamental model of collisional kinetic theory, and contains two distinct contributions to the subject
1 edition published in 2009 in English and held by 1 WorldCat member library worldwide
This thesis is devoted to the mathematical study of the Boltzmann equation, a fundamental model of collisional kinetic theory, and contains two distinct contributions to the subject
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