Non-uniformly elliptic problems

• Grant number: 24/04156-0
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2024
• End date: August 31, 2026
• 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 operators with non standard growth and/or non local nature. In particular, in this project we intend to work on the following directions.(1) In the first topic, with Prof. Csaba Farkas (Sapientia Hungarian University of Transylvania), Prof. Ky Ho (Ulsan National Institute of Science and Technology) and Prof. Patrick Winkert (Technische Universität Berlin) we will study multiplicity results for double phase problems involving critical Sobolev terms of double phase type. Instead, I will study a double phase problem involving singular Hardy potentials. Also, with Prof. Anouar Bahrouni (University of Monastir), we will consider a double phase equation set in the whole space RN, by adding a logarithmic term.(2) In the second topic, joint with Prof. Mousomi Bhakta (Indian Institute of Science Education and Research Pune) and Dr. Shilpa Gupta (Indian Institute of Science Education and Research Pune) we will study a fractional problem of (p,q) type and involving critical terms.(3) The third topic will be devoted to an anisotropic Kirchhoff problem, as studied by Prof. Leandro Tavares (Federal University of Cariri).(4) Finally, we will consider a possible fractional generalization of the double phase operator. (AU)