Elliptic regularity theory by approximation methods:
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, incl...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2022
|
| Schriftenreihe: | London Mathematical Society lecture note series
477 |
| Schlagworte: | |
| Online-Zugang: | BSB01 BTU01 FHN01 UBG01 Volltext |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 20 Jun 2022) |
| Beschreibung: | 1 Online-Ressource (xi, 190 Seiten) |
| ISBN: | 9781009099899 |
| DOI: | 10.1017/9781009099899 |
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| 520 | |a 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 | ||
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Datensatz im Suchindex
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| author | Pimentel, Edgard A. ca. 20./21. Jh |
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| dewey-full | 515.353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
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| dewey-search | 515.353 |
| dewey-sort | 3515.353 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| doi_str_mv | 10.1017/9781009099899 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9781009099899 |
| language | English |
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| physical | 1 Online-Ressource (xi, 190 Seiten) |
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| spelling | Pimentel, Edgard A. ca. 20./21. Jh. (DE-588)1248568915 aut Elliptic regularity theory by approximation methods Edgard A. Pimentel Cambridge Cambridge University Press 2022 1 Online-Ressource (xi, 190 Seiten) txt rdacontent c rdamedia cr rdacarrier London Mathematical Society lecture note series 477 Title from publisher's bibliographic system (viewed on 20 Jun 2022) 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 Partial differential equations alculus of variations Regularität (DE-588)4049074-9 gnd rswk-swf Elliptisches System (DE-588)4121184-4 gnd rswk-swf Elliptisches System (DE-588)4121184-4 s Regularität (DE-588)4049074-9 s DE-604 Erscheint auch als Druck-Ausgabe 978-1-00-909666-9 https://doi.org/10.1017/9781009099899 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Pimentel, Edgard A. ca. 20./21. Jh Elliptic regularity theory by approximation methods Partial differential equations alculus of variations Regularität (DE-588)4049074-9 gnd Elliptisches System (DE-588)4121184-4 gnd |
| subject_GND | (DE-588)4049074-9 (DE-588)4121184-4 |
| title | Elliptic regularity theory by approximation methods |
| title_auth | Elliptic regularity theory by approximation methods |
| title_exact_search | Elliptic regularity theory by approximation methods |
| title_exact_search_txtP | Elliptic regularity theory by approximation methods |
| title_full | Elliptic regularity theory by approximation methods Edgard A. Pimentel |
| title_fullStr | Elliptic regularity theory by approximation methods Edgard A. Pimentel |
| title_full_unstemmed | Elliptic regularity theory by approximation methods Edgard A. Pimentel |
| title_short | Elliptic regularity theory by approximation methods |
| title_sort | elliptic regularity theory by approximation methods |
| topic | Partial differential equations alculus of variations Regularität (DE-588)4049074-9 gnd Elliptisches System (DE-588)4121184-4 gnd |
| topic_facet | Partial differential equations alculus of variations Regularität Elliptisches System |
| url | https://doi.org/10.1017/9781009099899 |
| work_keys_str_mv | AT pimenteledgarda ellipticregularitytheorybyapproximationmethods |