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Více informací o knize Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit

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Anotace knihy

Fred Almgren created the excess method for proving regularity theorems in the calculus of variations. His techniques yielded Holder continuity 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 exposition 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.

Parametry knihy

Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Calculus & mathematical analysis

• Plný název: Almgren's Big Regularity Paper, Q-valued Functions Minimizing Dirichlet's Integral And The Regularit
• Autor: Vladimir Scheffer, Jean E. Taylor
• Jazyk: Angličtina
• Vazba: Pevná
• Počet stran: 972
• EAN: 9789810241087
• ISBN: 9810241089
• ID: 01367800
• Nakladatelství: World Scientific Publishing Co Pte Ltd
• Hmotnost: 1788 g
• Rozměry: 254 × 180 × 54 mm
• Datum vydání: 08. April 2000

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