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Nonlinear Elliptic Equations with Singular Potentials

Grant number: 12/10153-6
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): November 01, 2012
Effective date (End): July 31, 2013
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal researcher:Lucas Catão de Freitas Ferreira
Grantee:Sérgio Leandro Nascimento Neves
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we study two problems about elliptic partial differential equations with critical singular potential of Hardy type. They can be either isotropic or anisotropic, and polar (one singularity) or multipolar (finitely many singularities). In the first problem, we consider the potential and nonlinearity in the interior of a smooth domain, handling it by perturbation methods and Lyapunov-Schmidt reductions. In the second one, the potential, singularities and nonlinearity are on the boundary of the domain, and we intend to study it by means of the following approaches: minimization methods combined with Hardy inequality on the boundary; or fixed point arguments with integral formulations based on Green functions. We investigate the existence and uniqueness of solutions and their asymptotic behaviors near the singularities of the potential. Another considered approach for the two problems is through optimal mass transport techniques, in order to find solutions as steady states and asymptotic limits of the corresponding parabolic models.

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FERREIRA, LUCAS C. F.; NEVES, SERGIO L. N. ON ELLIPTIC EQUATIONS WITH SINGULAR POTENTIALS AND NONLINEAR BOUNDARY CONDITIONS. QUARTERLY OF APPLIED MATHEMATICS, v. 76, n. 4, p. 699-711, DEC 2018. Web of Science Citations: 0.
GLADIALI, FRANCESCA; GROSSI, MASSIMO; NEVES, SERGIO L. N. Symmetry breaking and Morse index of solutions of nonlinear elliptic problems in the plane. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, v. 18, n. 5 OCT 2016. Web of Science Citations: 3.
GLADIALI, FRANCESCA; GROSSI, MASSIMO; NEVES, SERGIO L. N. Nonradial solutions for the Henon equation in R-N. ADVANCES IN MATHEMATICS, v. 249, p. 1-36, DEC 20 2013. Web of Science Citations: 19.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.