Elliptic regularity theory by approximation methods /

Elliptic regularity theory by approximation methods /

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Bibliographic Details
Author / Creator:	Pimentel, Edgard A., author.
Imprint:	Cambridge : Cambridge University Press, 2022.
Description:	xi, 190 pages ; 23 cm.
Language:	English
Series:	London Mathematical Society Lecture Note Series ; 477 London Mathematical Society lecture note series ; 477.
Subject:	Elliptic functions. Elliptic functions.
Format:	Print Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/12917669

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ISBN:	9781009096669 9781009099899 9781009103121 1009096664
Notes:	Includes bibliographical references (pages 181-188) and index.
Summary:	"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."--
Other form:	Online version: Pimentel, Edgard A. Elliptic regularity theory by approximation methods. Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022 9781009099899 9781009103121

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Call Number:	QA343.P56 2022
c.1	Available Loan period: standard loan Request for Pickup Need help? - Ask a Librarian