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Elliptic Regularity Theory by Approximation Methods

Elliptic Regularity Theory by Approximation Methods

Elliptic Regularity Theory by Approximation Methods Paperback / softback - 2022

by Edgard A. Pimentel

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Details

  • Title Elliptic Regularity Theory by Approximation Methods
  • Author Edgard A. Pimentel
  • Binding Paperback
  • Condition New
  • Pages 202
  • Volumes 1
  • Language ENG
  • Publisher Cambridge University Press
  • Publication date 2022-09-29
  • Bookseller's Inventory # B9781009096669
  • ISBN 9781009096669 / 1009096664
  • Weight 0.65 lbs (0.29 kg)
  • Dimensions 8.9 x 5.9 x 0.5 in (22.61 x 14.99 x 1.27 cm)
  • Category Mathematics
  • Quantity available 10

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Reader reviews for Elliptic Regularity Theory by Approximation Methods

From the publisher

Presenting the basics of elliptic PDEs in connection with regularity theory, the book bridges fundamental breakthroughs - such as the Krylov-Safonov and Evans-Krylov results, Caffarelli's regularity theory, and the counterexamples due to Nadirashvili and Vlăduţ - and modern developments, including improved regularity for flat solutions and the partial regularity result. After presenting this general panorama, accounting for the subtleties surrounding C-viscosity and Lp-viscosity solutions, the book examines important models through approximation methods. The analysis continues with the asymptotic approach, based on the recession operator. After that, approximation techniques produce a regularity theory for the Isaacs equation, in Sobolev and Hlder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hlder continuity for the Hessian of the solutions by connecting the problem with a Bellman equation. To complete the book, degenerate models are studied and their optimal regularity is described.
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