检索结果-南通市图书馆

Chinese Annals of Mathematics,Series B 2017年第2期38卷 497-512页

作者： fanghua lin courant institute of mathematical sciences 251 Mercer StreetNew YorkNY.10012USA.

In this survey on extremum problems of Laplacian-Dirichlet eigenvalues of Euclidian domains, the author briefly presents some relevant classical results and recent progress. The main goal is to describe the well-known conjecture due to Polya, its connections to Weyl's asymptotic formula for eigenvalues and shape optimizations. Many related open problems and some preliminary results are also discussed.

关键词： Extremum problems, Laplacian eigenvalues, Weyl asymptotics, Polya'sconjecture, Spliting equality, Regularity of minimizers

On Regularity and Singularity of Free Boundaries in Obstacle Problems

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2009年第5期30卷 645-652页

作者： fanghua lin Courant Institute of Mathematical Sciences New York University 251 Mercer Street New York 10012 USA.

The author presents a simple approach to both regularity and singularity theorems for free boundaries in classical obstacle *** approach is based on the monotonicity of several variational integrals,the Federer-Almgre... 详细信息

关键词： Free boundary Monotonicity Dimension reduction Uniqueness of blow-ups

Boundary Harnack principle on nodal domains Dedicated to Professor Jiaxing Hong on the Occasion of His 80th Birthday

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2022年第12期65卷 2441-2458页

作者： fanghua lin Zhengjiang lin Courant Institute of Mathematical Sciences New York UniversityNewYorkNY10012USA

We study some geometric and potential theoretic properties of nodal domains of solutions to certain uniformly elliptic equations. In particular, we establish corkscrew conditions, Carleson type estimates and boundary ... 详细信息

关键词： boundary Harnack principle nodal domain modified Harnack chain Carleson type estimate frequency bound

Large m asymptotics for minimal partitions of the Dirichlet eigenvalue

在线全文

学校读者我要写书评

暂无评论

Science China Mathematics 2022年第1期65卷 1-8页

作者： Zhiyuan Geng fanghua lin Courant Institute of Mathematical Sciences New York UniversityNew YorkNY 10012USA

In this paper,we study large m asymptotics of the l 1 minimal m-partition problem for the Dirichlet *** any smooth domainΩ⊂R^(n)such that|Ω|=1,we prove that the limit lim_(m→∞)l^(1)_(m)(Ω)=c 0 exists,and the constant c 0 is independent of the shape ofΩ.Here,l^(1)_(m)(Ω)denotes the minimal value of the normalized sum of the first Laplacian eigenvalues for any m-partition ofΩ.

关键词： Dirichlet eigenvalue l1 minimal partition problem large m asymptotics

Harmonic Maps in Connection of Phase Transitions with Higher Dimensional Potential Wells

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2019年第5期40卷 781-810页

作者： fanghua lin Changyou WANG Courant Institute of Mathematical Sciences New York UniversityNY 10012USA Department of Mathematics Purdue UniversityWest LafayetteIN 47907USA.

This is in the sequel of authors’ paper [lin, F. H., Pan, X. B. and Wang, C. Y.,Phase transition for potentials of high dimensional wells, Comm. Pure Appl. Math., 65(6),2012, 833–888] in which the authors had set up a program to verify rigorously some formal statements associated with the multiple component phase transitions with higher dimensional wells. The main goal here is to establish a regularity theory for minimizing maps with a rather non-standard boundary condition at the sharp interface of the *** authors also present a proof, under simplified geometric assumptions, of existence of local smooth gradient flows under such constraints on interfaces which are in the motion by the mean-curvature. In a forthcoming paper, a general theory for such gradient flows and its relation to Keller-Rubinstein-Sternberg’s work(in 1989) on the fast reaction, slow diffusion and motion by the mean curvature would be addressed.

关键词： Partially free and partially constrained boundary Boundary partial regularity Boundary monotonicity inequality

Nodal Sets and Doubling Conditions in Elliptic Homogenization

在线全文

学校读者我要写书评

暂无评论

Acta Mathematica Sinica,English Series 2019年第6期35卷 815-831页

作者： fanghua lin Zhongwei Shen Courant Institute of Mathematical Sciences Department of Mathematics University of Kentucky

This paper is concerned with uniform measure estimates for nodal sets of solutions in elliptic homogenization. We consider a family of second-order elliptic operators {L_ε} in divergence form with rapidly oscillating and periodic coefficients. We show that the(d-1)-dimensional Hausdorff measures of the nodal sets of solutions to L_ε(u_ε) = 0 in a ball in Rdare bounded uniformly in ε > 0. The proof relies on a uniform doubling condition and approximation of u_ε by solutions of the homogenized equation.

关键词： Nodal sets homogenization doubling condition

On Current Developments in Partial Differential Equations

在线全文

学校读者我要写书评

暂无评论

Communications in Mathematical Research 2020年第1期36卷 1-30页

作者： fanghua lin Courant Institute New York UniversityNew YorkNY 10012USA.

The first part of this article is an overview on some recent major developments in the field of analysis and partial different *** is a brief presentation given by the author at a round table *** second part is a supp... 详细信息

关键词： Partial differential equations harmonic analysis geometric measure theory

On the Uniqueness of Heat Flow of Harmonic Maps and Hydrodynamic Flow of Nematic Liquid Crystals

在线全文

学校读者我要写书评

暂无评论

Chinese Annals of Mathematics,Series B 2010年第6期31卷 921-938页

作者： fanghua lin Changyou WANG Courant Institute of Mathematical Sciences New York University New York NY 10012 USA Department of Mathematics University of Kentucky Lexington KY 40506 USA.

For any n-dimensional compact Riemannian manifold (M,g) without boundary and another compact Riemannian manifold (N,h), the authors establish the uniqueness of the heat flow of harmonic maps from M to N in the class C([0,T),W1,n). For the hydrodynamic flow (u,d) of nematic liquid crystals in dimensions n = 2 or 3, it is shown that the uniqueness holds for the class of weak solutions provided either (i) for n = 2, u ∈ Lt∞ L2x∩L2tHx1, ▽P∈ Lt4/3 Lx4/3 , and ▽d∈ L∞t Lx2∩Lt2Hx2; or (ii) for n = 3, u ∈ Lt∞ Lx2∩L2tHx1∩ C([0,T),Ln), P ∈ Ltn/2 Lxn/2 , and ▽d∈ L2tLx2 ∩ C([0,T),Ln). This answers affirmatively the uniqueness question posed by lin-lin-Wang. The proofs are very elementary.

关键词： Hydrodynamic flow Harmonic maps Nematic liquid crystals Uniqueness

SEMICLASSICAL STATES OF HAMILTONIAN SYSTEM OF SCHROEDINGER EQUATIONS WITH SUBCRITICAL AND CRITICAL NONlinEARITIES

在线全文

学校读者我要写书评

暂无评论

Journal of Partial Differential Equations 2006年第3期19卷 232-255页

作者： Ding Yanheng lin fanghua Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100080 China. Courant Institute of Mathematical Sciences New York University New York NY 10012 USA

We consider the system of perturbed Schroedinger equations{-ε^2△φ＋α（x）φ=β（x）ψ＋Fψ（x,φ,ψ）-ε^2△ψ＋α（x）ψ=β（x）φ＋Fφ（x,φ,ψ）ω：=（φ,ψ）∈H^1（R^N,R^2）where N≥1, α and β are continuous real functions on R^N, and F ： R^N×R^2 → R is of class C^1. We assume that either F（x,ω） is super-quadratic and subcritical in ω∈R^2 or it is of the form ～1/P（x）｜ω｜^p ＋1/2^＊K（x）｜ω｜^2^＊ with p E （2,2^＊） and 2^＊ = 2N/（N-2）, the Sobolev critical exponent, P（x） and K（x） are positive bounded functions. Under proper conditions we show that the system has at least one nontrivial solution ωε provided ε≤ε; and for any m∈N, there are m pairs of solutions ωε provided that ε≤εm and that F（x, ω） is,in addition, even in ω. Here ε and ωε are sufficiently small positive numbers. Moreover, the energy of ωε tends to 0 as ε→0.

关键词： Perturbed Schrodinger equation critical nonlinearity multiple solutions.

Exponential Growth Solutions of Elliptic Equations

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

Acta Mathematica Sinica,English Series 1999年第4期15卷 525-534页

作者： Fengbo Hang fanghua lin Courant Institute,251 Mercer Street,New York,NY 10012,U S A E-mail:fengbo@cims.nyu.edu linf@cims.nyu.edu Courant Institute New York USA

We show that for a class of second order divergence form elliptic equations on an infinite strip with the Dirichlet boundary condition,the space of fixed order exponential growth solutions is of finite *** optimal estimation of the dimension is *** also show that the finiteness property may not be true if one drops some of the conditions we make in our result.

关键词： Elliptic equations Exponential growth function Poincarés inequality Mean value inequality