Maximum Principles And Harnack’s Inequality / Khadra Ikram Bekar  

Public ISBD Titre : Maximum Principles And Harnack’s Inequality Type de document : document électronique Auteurs : Khadra Ikram Bekar, Auteur ; Boutiah,Sallah Eddine, Directeur de thèse Editeur : Sétif:UFS Année de publication : 2026 Importance : 1 vol (52 f.) Format : 29 cm Note générale : Langues : Anglais (eng) Catégories : Mathématique Mots-clés : Maximum principles, Harnack inequality, Elliptic PDEs, Parabolic PDEs, Hopf’s lemma, Positive solutions Résumé : This thesis studies two fundamental principles in the theory of second-order elliptic and parabolic partial differential equations: the maximum principles and Harnack’s inequality. We prove the weak and strong maximum principles, using Hopf’s lemma to show that an interior maximum forces the solution to be constant. We then establish Harnack’s inequality, which provides quantitative comparison bounds for positive solutions. Starting from harmonic functions, we extend the result to elliptic operators with smooth coefficients, state Moser’s results for measurable coefficients, and prove the parabolic Harnack inequality. As an application, we use it to prove the strong maximum principle for parabolic operators. These results form a unified framework for understanding the regularity and pointwise behavior of solutions. Côte titre : MAM/0867 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/e1e22346-1bcc-49d7-a [...] Maximum Principles And Harnack’s Inequality [document électronique] / Khadra Ikram Bekar, Auteur ; Boutiah,Sallah Eddine, Directeur de thèse . - [S.l.] : Sétif:UFS, 2026 . - 1 vol (52 f.) ; 29 cm. Langues : Anglais (eng) Catégories : Mathématique Mots-clés : Maximum principles, Harnack inequality, Elliptic PDEs, Parabolic PDEs, Hopf’s lemma, Positive solutions Résumé : This thesis studies two fundamental principles in the theory of second-order elliptic and parabolic partial differential equations: the maximum principles and Harnack’s inequality. We prove the weak and strong maximum principles, using Hopf’s lemma to show that an interior maximum forces the solution to be constant. We then establish Harnack’s inequality, which provides quantitative comparison bounds for positive solutions. Starting from harmonic functions, we extend the result to elliptic operators with smooth coefficients, state Moser’s results for measurable coefficients, and prove the parabolic Harnack inequality. As an application, we use it to prove the strong maximum principle for parabolic operators. These results form a unified framework for understanding the regularity and pointwise behavior of solutions. Côte titre : MAM/0867 En ligne : https://repository.univ-setif.dz/server/api/core/bitstreams/e1e22346-1bcc-49d7-a [...]

Exemplaires (1)

Code-barres	Cote	Support	Localisation	Section	Disponibilité
MAM/0867	MAM/0867	Mémoire	Bibliothèque des sciences	Anglais	Disponible Disponible

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