Research | Mathematical Analysis

Reasearch topics

• Second order linear elliptic equations: a priori estimates, regularity, existence and uniqueness, weighted Sobolev spaces.
• Fully non-linear elliptic equations: qualitative properties, regularity, existence and uniqueness, removable singularities, viscosity solutions.
• Parabolic equations and semigroup theory.
• Regularity for equations and systems of PDEs.
• Symmetrization and isoperimetric inequalities.
• Free boundary problems.
• Classical and non-additive measure theory and applications to the study of function spaces.