Research Areas and Interests

My area of research is partial differential equations. The main line of my research is concerned with positive solutions of second order elliptic and parabolic equations. This topic is closely related to the study of the structure and of the asymptotic behavior of solutions of linear and nonlinear elliptic and parabolic equations which appear in many branches of mathematics. For instance, positive solutions play an important role in some problems in differential geometry, in the spectral theory of Schrödinger operators, in many questions in applied mathematics and in some problems in Markov process theory. The focus of my research is on representation theorems, Green’s functions and heat kernels estimates, Liouville theorems, variational principles, and removable singularities.