Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit (World Scientific Monograph Series In Mathematics

Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit (World Scientific Monograph Series In Mathematics

By: Vladimir Scheffer (author), Jean E. Taylor (author)Hardback

Up to 2 WeeksUsually despatched within 2 weeks

Description

Fred Almgren exploited the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Hoelder continuous differentiability except for a small closed singular set. In the sixties and seventies Almgren refined and generalized his methods. Between 1974 and 1984 he wrote a 1,700-page proof that was his most ambitious development of his ground-breaking ideas. Originally, this monograph was available only as a three-volume work of limited circulation. The entire text is faithfully reproduced here.This book gives a complete proof of the interior regularity of an area-minimizing rectifiable current up to Hausdorff codimension 2. The argument uses the theory of Q-valued functions, which is developed in detail. For example, this work shows how first variation estimates from squash and squeeze deformations yield a monotonicity theorem for the normalized frequency of oscillation of a Q-valued function that minimizes a generalized Dirichlet integral. The principal features of the book include an extension theorem analogous to Kirszbraun's theorem and theorems on the approximation in mass of nearly flat mass-minimizing rectifiable currents by graphs and images of Lipschitz Q-valued functions.

Product Details

  • ISBN13: 9789810241087
  • Format: Hardback
  • Number Of Pages: 972
  • ID: 9789810241087
  • ISBN10: 9810241089

Delivery Information

  • Saver Delivery: Yes
  • 1st Class Delivery: Yes
  • Courier Delivery: Yes
  • Store Delivery: Yes

Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly

Close