Geometric variational problems: existence, regularity and geometrical characteriza...
From the Integral Transforms to the Fractional Calculus applied to the Production ...
Variational studies for the nonlinear logarithmic Schrodinger equations
Grant number: | 17/19752-3 |
Support Opportunities: | Regular Research Grants |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Analysis |
Principal Investigator: | Alessio Fiscella |
Grantee: | Alessio Fiscella |
Host Institution: | Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil |
Abstract
This research project focuses on the study of nonlinear elliptic problems driven by nonlocal fractional operators with lack of compactness. In particular, in this project we intend to work on the following directions.(1) In the first topic, with Prof. Patrizia Pucci (Università degli Studi di Perugia) and Prof. Binlin Zhang (HeilongjiangInstitute of Technology) we will study existence results for fractional systems involving critical terms.(2) In the second topic, joint with Dr. Vincenzo Ambrosio (Università degli Studi Urbino "Carlo Bo") we will study multiplicity results for fractional problems involving a critical Sobolev term and a Hardy potential.(3) Joint with Dr. Pawan Mishra (Universidade Federal da Paraíba), we will try to study fractional Kirchhoff type problems involving a Sobolev term and a singular one.(4) Finally, with Prof. Andrea Pinamonti (Università degli Studi di Trento) and Dr. Eugenio Vecchi (Università degli Studi di Bologna) we want to extend some classical existence and multiplicity results, proved for the Laplacian and the fractional Laplacian, to the complex case of the fractional magnetic Laplacian. (AU)
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