Elliptic regularity theory by approximation methods
著者
書誌事項
Elliptic regularity theory by approximation methods
（London Mathematical Society lecture note series, 477）
Cambridge University Press, 2022
- : pbk
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注記
Includes bibliographical references (p. 181-188) and index
内容説明・目次
内容説明
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.
目次
- Preface
- 1. Elliptic partial differential equations
- 2. Flat solutions are regular
- 3. The recession strategy
- 4. A regularity theory for the Isaacs equation
- 5. Regularity theory for degenerate models
- References
- Index.
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