Elliptic Regularity Theory by Approximation Methods

By:

Edgard A. Pimentel

Format:

Paperback / softback

Series:

London Mathematical Society Lecture Note Series,

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Description

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 Hölder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hölder 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.

Author Biography:

Edgard A. Pimentel is Research Scientist at the University of Coimbra and Assistant Professor of Mathematics at Pontifical Catholic University of Rio de Janeiro. He is researcher for the National Council of Science and Technology (CNPq-Brazil), a junior associate fellow of the International Centre for Theoretical Physics, and an affiliated member of the Brazilian Academy of Sciences.

Release date Australia

September 29th, 2022

Author

Edgard A. Pimentel

Audience

Tertiary Education (US: College)

Illustrations

Worked examples or Exercises

Pages

202

Series

London Mathematical Society Lecture Note Series,

Dimensions

152x228x12

ISBN-13

9781009096669

Product ID

36398832

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