De Giorgi-Nas-Moser Theory3 / Kawthar Aliaoua

Public ISBD Titre : De Giorgi-Nas-Moser Theory3 Type de document : texte imprimé Auteurs : Kawthar Aliaoua, Auteur ; Boutiah,Sallah Eddine, Directeur de publication, rédacteur en chef Editeur : Sétif:UFS Année de publication : 2024 Importance : 1 vol (31 f.) Format : 29 cm Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Mathématique Index. décimale : 510-Mathématique Résumé : This chapter is interested in Sobolev spaces and their applications in solving elliptic partial differential equations (PDEs), focusing on regularity results for weak solutions of these equations. Key points: Introduction to Sobolev spaces: Definitions and fundamental properties of Sobolev spaces, essential for the study of weak PDE solutions. Weak solutions of elliptic PDEs: Definition of weak solutions for elliptic PDEs of the form div(A(x)∇u(x)) = 0. Moser Iteration: Presentation of Moser iteration, a technique for proving regularity results for weak solutions of elliptic PDEs. The chapter provides a solid foundation for understanding the use of Sobolev spaces in the study of weak solutions of elliptic PDEs. The following sections will delve deeper into the regularity aspects using Moser's iteration and Harnack's inequality. Note de contenu : Sommaire 1 GeneralIntroduction 5 2 Motivation:avariationalproblem 7 3 Preliminaryfactson Lp spaces andSobolevspaces 11 3.1 Definitionandsomebasicproperties . ..................... 11 3.1.1 Lp Spaces . ................................ 12 3.2 AbriefintroductiontoSobolevspaces . .................... 12 3.2.1 H¨olderspace . .............................. 12 3.2.2 Weakderivatives . ............................ 12 3.2.3 Inequalities . ............................... 13 3.3 Weakcompactnesstheorem . .......................... 14 3.3.1 Differencequotients . .......................... 14 3.4 Definitionofweaksolutions . .......................... 15 4 Moser’siteration 17 4.1 Harnack’sinequality . .............................. 17 4.1.1 WeakHarnack’sinequality:Sup . ................... 18 4.1.2 WeakHarnack’sinequality:Inf . .................... 24 5 DeGiorgi’smethod 27 5.0.1 DeGiorgi’sclassoffunctions . ..................... 27 5.1 Boundednessoffunctionsin DG(Ω, γ) . .................... 27 Côte titre : MAM/0702 De Giorgi-Nas-Moser Theory3 [texte imprimé] / Kawthar Aliaoua, Auteur ; Boutiah,Sallah Eddine, Directeur de publication, rédacteur en chef . - [S.l.] : Sétif:UFS, 2024 . - 1 vol (31 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Thèses & Mémoires:Mathématique Mots-clés : Mathématique Index. décimale : 510-Mathématique Résumé : This chapter is interested in Sobolev spaces and their applications in solving elliptic partial differential equations (PDEs), focusing on regularity results for weak solutions of these equations. Key points: Introduction to Sobolev spaces: Definitions and fundamental properties of Sobolev spaces, essential for the study of weak PDE solutions. Weak solutions of elliptic PDEs: Definition of weak solutions for elliptic PDEs of the form div(A(x)∇u(x)) = 0. Moser Iteration: Presentation of Moser iteration, a technique for proving regularity results for weak solutions of elliptic PDEs. The chapter provides a solid foundation for understanding the use of Sobolev spaces in the study of weak solutions of elliptic PDEs. The following sections will delve deeper into the regularity aspects using Moser's iteration and Harnack's inequality. Note de contenu : Sommaire 1 GeneralIntroduction 5 2 Motivation:avariationalproblem 7 3 Preliminaryfactson Lp spaces andSobolevspaces 11 3.1 Definitionandsomebasicproperties . ..................... 11 3.1.1 Lp Spaces . ................................ 12 3.2 AbriefintroductiontoSobolevspaces . .................... 12 3.2.1 H¨olderspace . .............................. 12 3.2.2 Weakderivatives . ............................ 12 3.2.3 Inequalities . ............................... 13 3.3 Weakcompactnesstheorem . .......................... 14 3.3.1 Differencequotients . .......................... 14 3.4 Definitionofweaksolutions . .......................... 15 4 Moser’siteration 17 4.1 Harnack’sinequality . .............................. 17 4.1.1 WeakHarnack’sinequality:Sup . ................... 18 4.1.2 WeakHarnack’sinequality:Inf . .................... 24 5 DeGiorgi’smethod 27 5.0.1 DeGiorgi’sclassoffunctions . ..................... 27 5.1 Boundednessoffunctionsin DG(Ω, γ) . .................... 27 Côte titre : MAM/0702

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Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0702	MAM/0702	Mémoire	Bibliothéque des sciences	Anglais	Disponible Disponible

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