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Elliptic regularity theory by approximation methods

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Elliptic regularity theory by approximation methods/ Edgard A. Pimentel.
作者:	Pimentel, Edgard A.
出版者:	Cambridge :Cambridge University Press, : 2022.,
面頁冊數:	xi, 190 p. :ill., digital ; : 23 cm.;
附註:	Title from publisher's bibliographic system (viewed on 20 Jun 2022).
標題:	Partial differential equations. -
電子資源:	https://doi.org/10.1017/9781009099899
ISBN:	9781009099899

Elliptic regularity theory by approximation methods
Pimentel, Edgard A.

Elliptic regularity theory by approximation methods[electronic resource] /Edgard A. Pimentel. - Cambridge :Cambridge University Press,2022. - xi, 190 p. :ill., digital ;23 cm. - London Mathematical Society lecture note series ;477. - London Mathematical Society lecture note series ;382..

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.

ISBN: 9781009099899Subjects--Topical Terms:

1102982
Partial differential equations.

LC Class. No.: QA343 / .P56 2022

Dewey Class. No.: 515.983

Elliptic regularity theory by approximation methods
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490 1 $a London Mathematical Society lecture note series ; $v 477
500 $a Title from publisher's bibliographic system (viewed on 20 Jun 2022).
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.
650 0 $a Partial differential equations. $3 1102982
650 0 $a alculus of variations. $3 1405727
830 0 $a London Mathematical Society lecture note series ; $v 382. $3 773477
856 4 0 $u https://doi.org/10.1017/9781009099899