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.
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.
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
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
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 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...
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.
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...
We study the distance function to the boundary, Finsler geometry and the singular set of viscosity solutions of some Hamilton-Jacobi equations.
A convex Darboux Theorem (2002)
Ekeland, Ivar, Nirenberg, Louis
We give necessary and sufficent conditions for a smooth, generic, differential one-form w on Rn to decompose into a sum w = a1du1 +... +akduk, where the function a l are positive and the ul convex...
Decay of entropy solutions of nonlinear conservation laws (1999)
Gui-qiang Chen, Hermano Frid, Dedicated Peter, D. Lax, Louis Nirenberg
We are concerned with the asymptotic behavior of entropy solutions of nonlinear conservation laws. The main objective of this paper is to present an analytical approach and to explore its...
Techniques in Linear and Nonlinear Partial Differential Equations. (1998)
Much work has been done, especially for nonlinear, involving new a priori estimates, variational methods and Brownian motion. The author and collaborators have written a series of papers on fully...
Techniques in Linear and Nonlinear Partial Differential Equations. (1998)
The sliding method has been introduced, and the method of moving planes has been greatly extended and improved. These methods have been applied to a number of problems for fully nonlinear second...
Techniques in Linear and Nonlinear PDE's (1998)
Problems studied included existence and properties of solutions of nonlinear partial differential equations, including applications to shock waves and to differential geometry covering a very wide...
Degree Theory beyond Continuous Maps (1996)
u , in terms of local coordinates near x j and near y, is nonsingular at each x j . If we choose local coordinates compatible with the given orientations on X and Y , then degree of u at y, denoted...
The Dirichlet Problem for the Degenerate Monge-Ampère Equation. (1986)
Nirenberg, Louis, Caffarelli, E., Spruck, J.
Let O be a bounded convex domain in Rn with smooth, strictly convex boundary ¶O, i.e. the principal curvatures of ¶O are all positive. We study the problem of finding a convex function u in O such...
Lectures on linear partial differential equations : by Louis Nirenberg (1973)
"Expository lectures from the CBMS regional conference held at the Texas Tech University, May 22-26, 1972"