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Elliptic Regularity Theory by Approximation Methods
Paperback / softback
Main Details
Title |
Elliptic Regularity Theory by Approximation Methods
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Authors and Contributors |
By (author) Edgard A. Pimentel
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Series | London Mathematical Society Lecture Note Series |
Physical Properties |
Format:Paperback / softback | Pages:202 | Dimensions(mm): Height 228,Width 152 |
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Category/Genre | Calculus and mathematical analysis |
ISBN/Barcode |
9781009096669
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Classifications | Dewey:515.983 |
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Audience | Tertiary Education (US: College) | |
Illustrations |
Worked examples or Exercises
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Publishing Details |
Publisher |
Cambridge University Press
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Imprint |
Cambridge University Press
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Publication Date |
29 September 2022 |
Publication Country |
United Kingdom
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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 Vladut - 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 Hoelder spaces. Although the Isaacs operator lacks convexity, approximation methods are capable of producing Hoelder 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.
Reviews'The regularity theory of elliptic partial differential equations is one of the bedrocks of modern mathematics since it elegantly and creatively uses virtually all possible mathematical tools to construct a solid set of concepts with ubiquitous applications. This book tells a story about this regularity theory, especially from the point of view of viscosity solutions for fully nonlinear equations and in the light of perturbative methods. As all good stories, the important part is not the happy ending in itself, but the whole plot through the series of adventures and vicissitudes (namely, the beautiful theorems) in which the reader will be captured page after page.' Enrico Valdinoci, University of Western Australia
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