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.
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