Veuillez utiliser cette adresse pour citer ce document :
http://dspace1.univ-tlemcen.dz/handle/112/22729
Titre: | Nonlinear elliptic problems in relation with the fractional Laplacian : Existence and regularity |
Auteur(s): | ABDELBADIE, YOUNES |
Mots-clés: | Fractional Laplacian, fractional Poisson problem, Calderón-Zygmund, fractional KPZ-type problem, non local gradient, existence and non-existence results, Hardy potential. |
Date de publication: | 9-jui-2023 |
Editeur: | University of tlemcen |
Collection/Numéro: | 018 doct maths; |
Résumé: | In this thesis, we investigate nonlinear elliptic problems involving the fractional Laplacian operator. First of all, we give a global fractional Calderón Zygmund regularity theory for the fractional Poisson problem. Our proofs are based on a pointwise estimate of the fractional gradient of the Green’s function associated to the fractional Laplacian. As an application, using a fixed point argument, we derive existence results for some fractional KPZ-type problems (equation and system), with nonlocal gradient terms. Moreover, non-existence results are also given for the problems in question. Finally, we study the impact of a Hardy potential’s presence on our previous regularity and existence results. |
URI/URL: | http://dspace1.univ-tlemcen.dz/handle/112/22729 |
Collection(s) : | Doctorat LMD en en Physique |
Fichier(s) constituant ce document :
Fichier | Description | Taille | Format | |
---|---|---|---|---|
Nonlinear_elliptic_problems_in_relationwith_the_fractional_Laplacian__Existence_and_regularity.pdf | 758,21 kB | Adobe PDF | Voir/Ouvrir |
Tous les documents dans DSpace sont protégés par copyright, avec tous droits réservés.