Han, Zheng-Chao, Li, YanYan, Teixeira, Eduardo V.
$\sigma_k$-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In an earlier work YanYan Li proved that an admissible solution with an isolated...
Partial results on extending the Hopf Lemma (2009)
In [1], Theorem 3, the authors proved, in one dimension, a generalization of the Hopf Lemma, and the question arose if it could be extended to higher dimensions. In this paper we present two...
We present several results, including some remarks on the Hopf Lemma.
Bao, Ellen ShiTing, Li, YanYan, Yin, Biao
In this paper, we study the perfect and the insulated conductivity problems with multiple inclusions imbedded in a bounded domain in $\mathbb{R}^n, n\ge 2$. For these two extreme cases of the...
DOI: 10.1007/s00526-003-0230-0 (2009)
Let (M,g) be an n−dimensional, smooth, compact Riemannian manifold without boundary. For n =2, the uniformization theorem of Poincaré gives the existence of Riemannian metrics which are pointwise...
RESULTS ON POSITIVE SOLUTIONS OF ELLIPTIC EQUATIONS WITH A CRITICAL HARDY-SOBOLEV OPERATOR ∗ (2009)
Dedicated to Neil Trudinger with respect and friendship on the occasion of his sixty fifth birthday Key words. Hardy-Sobolev operator, uniqueness, entire solutions. AMS subject classifications....
Some remarks on singular solutions of nonlinear elliptic equations. I (2009)
Caffarelli, Luis, Li, YanYan, Nirenberg, Louis
The paper concerns singular solutions of nonlinear elliptic equations.
Assessing Collaborative Process in CSCL with an Intelligent Content Analysis (2009)
Yanyan Li, Jing Wang, Jian Liao, Donglun Zhao, Ronghuai Huang
Unveiling the collaborative process is of central importance in CSCL research. This paper firstly reviews the different methods to assess the collaborative process and corresponding supporting tools,...
Starshaped compact hypersurfaces with prescribed m-th mean curvature in elliptic space (2009)
Abstract. In this paper we consider the problem of finding a star-shaped compact hypersurface with prescribed k-th mean curvature in hyperbolic space. Under some sufficient conditions, we obtain an...
Of Jörgens, L. Caffarelli, Yanyan Li
A classical theorem of Jörgens (n = 2 [17]), Calabi (n ≤ 5 [7]), and Pogorelov (n ≥ 2 [18]) states that any classical convex solution of (1.1) det(D 2 u) = 1 inR n must be a quadratic...
Adaptive e-Learning in Knowledge Grid Environment (2008)
Knowledge Grid is a platform that enables uniform and effective knowledge sharing and management across the Internet. Based on it, this paper proposes an adaptive e-Learning in China Knowledge Grid...
A SHARP SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS ∗ (2008)
Abstract. Let (M, g) be a smooth compact Riemannian manifold without boundary of dimension n ≥ 6. We prove that
TOPOLOGY AND SOBOLEV SPACES (2008)
Let M and N be compact 1 connected oriented smooth Riemannian manifolds with or without boundary. Throughout the paper we assume that dimM ≥ 2 but dimN could possibly be one, for example N = S 1 is...
We establish Liouville theorems for C 1,1 loc, entire solutions and locally Lipschitz entire weak solutions to general degenerate conformally invariant fully nonlinear elliptic equations of second...
This paper is concerned with viscosity solutions of Hamilton-Jacobi (H-J) equations of the form (1.1) H(x, u,∇u) = 1 in�, a C 2,1 bounded domain (connected open set) in R n,and
n − 2 n+2 (1.1) −�u = u n−2 on R 2 n. The celebrated Liouville-type theorem of Caffarelli, Gidas, and Spruck [1] asserts
Yanyan Li, Louis Nirenberg, Dedicated Djairo, De Figueiredo
The well-known inequality refers to a nonnegative C 2 function u defined on an interval (−R, R). The inequality is in:
DEGREE AND SOBOLEV SPACES (2008)
Haïm Brezis, Yanyan Li, Petru Mironescu, Louis Nirenberg
Dedicated to Jurgen Moser in friendship and admiration
J. Eur. Math. Soc. 8, 295–316 c ○ European Mathematical Society 2006 (2008)
A fully nonlinear version of the
In the closure D of a bounded domain in Rn, we consider a composite media whose physical characteristics are smooth in the closures of subdomains Dm but possibly discontinuous across their...
A Proxy-Based Dynamic Inheritance of Soft-Device (2008)
Jia Bi, Yanyan Li, Yunpeng Xing, Xiang Li, Xue Chen
Abstract. Soft-device is a promising infrastructure of next-generation distributed system. Soft-devices are configurable and adaptive software virtual mechanism, providing services to each other and...
A PRIORI BOUNDS FOR CO-DIMENSION ONE ISOMETRIC EMBEDDINGS (2008)
Abstract. Let X: ( � n, g) → � n+1 be a � 4 isometric embedding of a � 4 metric g of non-negative sectional curvature on � n into the Euclidean space � n+1. We prove a priori bounds for...
This paper proposes a document logistics approach for cooperative research based on the Web and Knowledge Grid. The approach realizes effective research document collection, organization and...
Chruściel, Piotr T., Li, Yanyan, Weinstein, Gilbert
We extend the validity of Dain's angular-momentum inequality to maximal, asymptotically flat, initial data sets on a simply connected manifold with several asymptotically flat ends which are...
USA-Chile Workshop on Nonlinear Analysis, (2007)
ftp ejde.math.swt.edu or ejde.math.unt.edu (login: ftp) Gluing approximate solutions of minimum type on the Nehari manifold
The Hopf Lemma for second order elliptic operators is proved to hold in domains with $C^{1,\alpha}$, and even less regular, boundaries. It need not hold for $C^1$ boundaries. Corresponding results...
Symmetry and Asymmetry: The Method of Moving Spheres (2007)
Jin, Qinian, Li, Yanyan, Xu, Haoyuan
We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results....
IN-BETWEEN SPACE - MUSEUM OF CHINESE TEA (2007)
Project: museum of Chinese tea. Site: in Chinatown of Washington DC. Thesis: What is in-between space? How is in-between space designed in the museum of tea? How to create the feature for different...
IN-BETWEEN SPACE - MUSEUM OF CHINESE TEA (2007)
Project: museum of Chinese tea. Site: in Chinatown of Washington DC. Thesis: What is in-between space? How is in-between space designed in the museum of tea? How to create the feature for different...
A classical theorem of Liouville says: (2007)
Local gradient estimates of solutions to some
SYMMETRY AND ASYMMETRY: THE METHOD OF MOVING SPHERES (2007)
Qinian Jin, Yanyan Li, Haoyuan Xu
In this paper we will consider some nonlinear elliptic equations on R n and S n. We first consider (1.1) ∆u + c |x | 2u + u(n+2)/(n−2) = 0 and u> 0 in R n \{0}.
Gradient Estimates for the Perfect Conductivity Problem (2006)
Bao, Ellen Shiting, Li, YanYan, Yin, Biao
This paper concerns optimal gradient estimates of solutions for the perfect conductivity problem with closely spaced interfacial boundaries. The problem arises from composite material. Our estimates...
Compactness of solutions to the Yamabe problem. III (2006)
For a sequence of blow up solutions of the Yamabe equation on non-locally confonformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic...
Some Liouville theorems and applications (2006)
We give exposition of a Liouville theorem established in \cite{Li3} which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the...
Local gradient estimates of solutions to some conformally invariant fully nonlinear equations (2006)
This paper concerns local gradient estimates to solutions of general conformally invariant fully nonlinear elliptic equations of second order.
Jin, Qinian, Li, Aobing, Li, YanYan
This paper concerns a fully nonlinear version of the Yamabe problem on manifolds with boundary. We establish some existence results and estimates of solutions.
A geometric problem and the Hopf Lemma. II (2006)
A classical result of A.D. Alexandrov states that a connected compact smooth $n-$dimensional manifold without boundary, embedded in $\Bbb R^{n+1}$, and such that its mean curvature is constant, is a...
In-between space Museum of Chinese Tea / (2006)
Thesis (M. Arch.)--Virginia Polytechnic Institute and State University, 2006.
DOI 10.1007/s00526-006-0057-6 Calculus of Variations (2006)
Qinian Jin, Aobing Li, Yanyan Li
Estimates and existence results for a fully nonlinear
Yanyan Li, Presented Haïm Brezis
We establish local gradient estimates to solutions of general conformally invariant fully nonlinear second order elliptic equations.
In-between space [electronic resource] : Museum of Chinese Tea / (2006)
Project: museum of Chinese tea. Site: in Chinatown of Washington DC. Thesis: What is in-between space? How is in-between space designed in the museum of tea? How to create the feature for different...
Regularity of the distance function to the boundary (2005)
Let $\Omega$ be a domain in a smooth complete Finsler manifold, and let $G$ be the largest open subset of $\Omega$ such that for every $x$ in $G$ there is a unique closest point from $\partial...
A geometric problem and the Hopf Lemma. I (2005)
This, and its sequel, concern some variations of a classical theorem of A.D. Alexandrov and teh Hopf Lemma.
Starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space (2005)
We study the existence of starshaped compact hypersurfaces with prescribed m-th mean curvature in hyperbolic space.
Some multi-valued solutions to Monge-Ampere equations (2005)
We construct several types of multi-valued solutions to the Monge-Ampere equation in higher dimensions.
Conformally invariant fully nonlinear elliptic equations and isolated singularities (2005)
We study solutions to conformally invariant equations with isolated singularties.
Degenerate conformally invariant fully nonlinear elliptic equations (2005)
We establish Liouville type theorems for degenerate conformally invariant equations.
NONEXISTENCE OF POSITIVE SOLUTIONS FOR SOME FULLY NONLINEAR ELLIPTIC EQUATIONS ∗ (2005)
Qinian Jin, Yanyan Li, Haoyuan Xu, Q. Jin, Y. Li, H. Xu
Key words. Fully nonlinear elliptic equations, nonexistence, comparison principle AMS subject classifications. 35J60 It is well known that ∆u ≥ u p in R n has no positive solution if p> 1. For...
J. Eur. Math. Soc. 8, 317–339 c ○ European Mathematical Society 2006 (2005)
Abstract. A classical result of A. D. Alexandrov states that a connected compact smooth n-dimensional manifold without boundary, embedded in R n+1, and such that its mean curvature is constant, is a...
Compactness of solutions to the Yamabe problem. II (2004)
We study compactness of solutions to the Yamabe problem on Riemannian manifolds which are not locally conformally flat.
The Yamabe problem concerns finding a conformal metric on a given closed Riemannian manifold so that it has constant scalar curvature. This paper concerns mainly a fully nonlinear version of the...
Calc. Var. 24, 185–237 (2005) Calculus of Variations DOI: 10.1007/s00526-004-0320-7 (2004)
Let (M n,g) be a compact, smooth, connected Riemannian manifold (without boundary) of dimension n ≥ 3. The Yamabe conjecture has been proved through the works of Yamabe [92], Trudinger [91], Aubin...
Remark on some conformally invariant integral equations: the method of moving spheres (2003)
We study some conformally invariant integral equations using the method of moving spheres.
We study the distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations.
On some conformally invariant fully nonlinear equations (2003)
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully...
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
A general Liouville type theorem for some conformally invariant fully nonlinear equations (2003)
We establish a general Liouville type theorem for conformally invariant fully nonlinear equations.
Liouville type theorems and Harnack type inequalities for semilinear elliptic equations (2003)
Dedicated with admiration to L. Nirenberg on his seventy-fifth birthday 1
The voltage-gated potassium channel Kv1.3 regulates energy homeostasis and body weight (2003)
Xu, Jianchao, Koni, Pandelakis A., Wang, Peili, Li, Guoyong, Kaczmarek, Leonard, Wu, Yanling, ...
Voltage-gated potassium (Kv) channels regulate cell membrane potential and control a variety of cellular processes. Kv1.3 channels are expressed in several tissues and believed to participate in cell...
A Liouville type theorem for some conformally invariant fully nonlinear equations (2002)
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
A fully nonlinear version of the Yamabe problem and a Harnack type inequality (2002)
We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic equations.
A sharp Sobolev inequality on Riemannian manifolds (2002)
Let (M,g) be a smooth compact Riemannian manifold without boundary of dimension n>=6. We prove that {align*} \|u\|_{L^{2^*}(M,g)}^2 \le K^2\int_M\{|\nabla_g u|^2+c(n)R_gu^2\}dv_g...
Antonio Ambrosetti, Yanyan Li, Andrea Malchiodi
In this paper we prove some existence results concerning a problem arising in conformal differential geometry. Consider a smooth metric g on B ={x ∈ Rn: |x | < 1},the unit ball on Rn, n ≥...
Gluing approximate solutions of minimum type on the Nehari manifold (2001)
In the last decade or so, variational gluing methods have been widely used to construct homoclinic and heteroclinic type solutions of nonlinear elliptic equations and Hamiltonian systems. This note...
Multi-Name Credit Derivatives (2001)
Campbell, Kristen, Chen, Yun, Edwards, David A., Li, Yanyan, O’Connell, Sean, Patterson, Ryshon, ...
The problem addressed in this report is that of pricing multi-name credit derivatives. These are default guarantee contracts on a basket of “names” whose default rates are correlated.
A priori bounds for co-dimension one isometric embeddings (1999)
Li, Yanyan., Weinstein, Gilbert.
American Journal of Mathematics - Volume 121, Number 5, October 1999
A Priori Bounds For Co-Dimension One Isometric Embeddings (1999)
. Let X : (S n ; g) ! R n+1 be a C 4 isometric embedding of a C 4 metric g of non-negative sectional curvature on S n into the Euclidean space R n+1 . We prove a priori bounds for the trace of the...
A priori bounds for co-dimension one isometric embeddings (1998)
Li, Yanyan, Weinstein, Gilbert
We prove a priori bounds for the trace of the second fundamental form of a $C^4$ isometric embedding into $R^{n+1}$ of a metric $g$ of non-negative sectional curvature on $S^n$, in terms of the...
Monge Ampere Equations on Riemannian Manifolds (1996)
The main purpose of this paper is to study the Dirichlet problem for Monge Ampere equations on Riemannian manifolds. Let M n be a smooth Riemannian manifold of dimension n 2 and 0/M n a compact...
estimates for solutions of a problem of Alexandrov (1996)
this paper that when the density of ¯ is smooth and nonnegative, solutions to the Alexandrov problem are at least C
Mathematical Physics © Springer-Verlag 1994 On Diameters of Uniformly Rotating Stars (1993)
Abstract: In this paper we study the compressible fluid model of uniformly rotating starts. It was proved in [Li] that for a given mass, there exists an equilibrium solution to the problem if the...
Some nonlinear elliptic equations from geometry
We describe some recent work on certain nonlinear elliptic equations from geometry. These include the problem of prescribing scalar curvature on 𝕊n, the Yamabe problem on manifolds with boundary,...
The voltage-gated potassium channel Kv1.3 regulates peripheral insulin sensitivity
Xu, Jianchao, Wang, Peili, Li, Yanyan, Li, Guoyong, Kaczmarek, Leonard K., Wu, Yanling, ...
Kv1.3 is a voltage-gated potassium (K) channel expressed in a number of tissues, including fat and skeletal muscle. Channel inhibition improves experimental autoimmune encephalitis, in part by...
Renalase is a novel, soluble monoamine oxidase that regulates cardiac function and blood pressure
Xu, Jianchao, Li, Guoyong, Wang, Peili, Velazquez, Heino, Yao, Xiaoqiang, Li, Yanyan, ...
The kidney not only regulates fluid and electrolyte balance but also functions as an endocrine organ. For instance, it is the major source of circulating erythropoietin and renin. Despite currently...
Some nonlinear elliptic equations from geometry
We describe some recent work on certain nonlinear elliptic equations from geometry. These include the problem of prescribing scalar curvature on 𝕊n, the Yamabe problem on manifolds with boundary,...
The voltage-gated potassium channel Kv1.3 regulates peripheral insulin sensitivity
Xu, Jianchao, Wang, Peili, Li, Yanyan, Li, Guoyong, Kaczmarek, Leonard K., Wu, Yanling, ...
Kv1.3 is a voltage-gated potassium (K) channel expressed in a number of tissues, including fat and skeletal muscle. Channel inhibition improves experimental autoimmune encephalitis, in part by...
Renalase is a novel, soluble monoamine oxidase that regulates cardiac function and blood pressure
Xu, Jianchao, Li, Guoyong, Wang, Peili, Velazquez, Heino, Yao, Xiaoqiang, Li, Yanyan, ...
The kidney not only regulates fluid and electrolyte balance but also functions as an endocrine organ. For instance, it is the major source of circulating erythropoietin and renin. Despite currently...