UCLA Dept. of Mathematics
Distinguished Lecture Series (DLS)
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  Louis Nirenberg      

Professor Louis Nirenberg
Courant Institute, NYU
Lecture Locations: All Nirenberg lectures in MS 6627

Date: Tuesday, Nov. 12: 2 p.m. - 3 p.m.
Title: A problem on differential forms arising in economics.

Abstract: The solution to the following purely local problem is presented. Given a smooth vector field $v$ near the origin in $\Bbb R^n$, for $k =$ integer $< n$, when can one represent $v$ in the form $v = \Sigma^k_1 a_j \nabla u_j$ with $a_j(x) > 0$ and $u_j$ strictly convex, $1 \leq j \leq k$?

Date: Friday, Nov. 15: 3 p.m. - 4 p.m.
Title: And the planes still move.

Abstract: The method of moving planes is extremely useful in proving symmetry and monotonicity of solutions of some second order elliptic equations. In this talk some new uses are presented.

Date: Tuesday, Nov. 19: 2 p.m. - 3 p.m.
Title: Estimates for elliptic systems for composite material.

Abstract: We consider a domain D subdivided into subdomains $D_i$, and an elliptic system with smooth coefficients in each $D_i$ but which may jump from one $D_i$ to another. This arises in problems in elasticity for composite material. Estimates for $C^{1,\alpha}$ norms in each $D_i$ are obtained for solutions - independent of how close the $D_i$ are to each other.

Colloquium: Thursday: Nov. 21: 4 p.m. - 5 p.m.
Title: On the distance function to the boundary cut locus, and some Hamilton-Jacobi equations

Abstract: In a smooth domain we consider the distance function u to the boundary. The complement of the largest open subset in which u is smooth is called the ridge. It is shown that the map from a boundary point y, along interior normal, until it first hits the ridge, is Lipschitz continuous in y. This is then extended to a class of Hamilton-Jacobi equations to give information on the set where the solution is singular.

Background:

Louis Nirenberg is one of the outstanding analysts of the twentieth century. He has made fundamental contributions to the understanding of linear and nonlinear partial differential equations and their application to complex analysis and geometry.

Nirenberg received the AMS Bocher Prize in 1959 for his work on partial differential equations. In 1982 he was the first recipient in mathematics of the Crafoord Prize, established by the Royal Swedish Academy of Sciences in areas not covered by the Nobel Prizes. In 1995 he received the National Medal of Science, the United States' highest honor for contributions to science. (from Notices of the AMS, 4/2002)

More biographical information on Professor Nirenberg:
Notices of the AMS: April 2002, vol. 49, Number 4. (PDF File)


 

 

  
  
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