Pseudo-Gradient Flows for Nonsmooth Functionals

• Grant number: 11/19773-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: March 01, 2012
• End date: January 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Marcelo da Silva Montenegro
• Grantee: Adilson Eduardo Presoto
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project, we will study nonsmooth energy functionals associated to semilinear problems. In this situation, the classical techniques of variational methods do not apply. To overcome this difficulty, by using the differentiability in some directions, we will construct pseudo-gradient flows for these functionals and do a analysis, with the aim of to finding critical points. In this way, we will obtain results of existence and multiplicity of solutions for the semlinear problem.