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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

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