Discourses in Mathematics and Its Applications, No. 3 1994

A Tribute to Ilya Bakelman

Edited by I. R. Bakelman, S. A. Fulling, and S. D. Taliaferro

Contents

Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Program of the Symposium in Memory of Ilya Bakelman . . . . . . . . . . iv Message from the Mathematicians of St. Petersburg . . . . . . . . . . . 1 Ilya Bakelman in Russia . . . . . . . . . . . . . . . . . . . . . . . . 2

Mikhail S. Birman Ilya Bakelman in Texas . . . . . . . . . . . . . . . . . . . . . . . . 5

William L. Perry Piecewise-Polynomial Approximation of Functions from Sobolev

Spaces, Revisited . . . . . . . . . . . . . . . . . . . . . . . . . . 7

Michael Solomyak My Recollections of Ilya Bakelman . . . . . . . . . . . . . . . . . . . 28

Michael Solomyak Potential Theory of the Monge-Ampère Equation on a Banach Space …. 31

E.M.J. Bertin Message from Yu.G. Reshetnyak . . . . . . . . . . . . . . . . . . . . 36 On the Contact Angle in Capillarity II . . . . . . . . . . . . . . . . . 37

Robert Finn Isoperimetric Inequalities and Monge-Ampère Equations . . . . . . . . . 43

Neil S. Trudinger Generalized Solutions of Monge-Ampere Equations of Elliptic Type . . . . . 47

A.V. Pogorelov

(continued)

A Simple Proof of the Birkhoff-von Neumann Theorem

on Bistochastic Matrices . . . . . . . . . . . . . . . . . . . . . . . 51

Joseph V. Romanovsky Message from Umberto Mosco . . . . . . . . . . . . . . . . . . . . . 54 Non-existence of Positive Solutions of Semilinear Elliptic Systems . . . . . . 55

James Serrin and Henghui Zou Worn Stones with Flat Sides . . . . . . . . . . . . . . . . . . . . . . 69

Richard S. Hamilton Harmonic Maps on Complete Noncompact Riemannian Manifolds . . . . . . 79

Wanxiong Shi and S.T. Yau Finite Element Analysis for Wave Propagation in Inhomogeneous

Elastic Media . . . . . . . . . . . . . . . . . . . . . . . . . . . 121

Zhangxin Chen Message from Louis Nirenberg . . . . . . . . . . . . . . . . . . . . 135 Resolution of the Regents of Texas A&M University . . . . . . . . . . . 136 Response of Irene and Alexander Bakelman . . . . . . . . . . . . . . 137