Radial singular solutions of fully nonlinear equations in punctured balls

par Prof. Fabiana Leoni (Université Rome La Sapienza)

jeudi 14 nov. 2024, 13:30 → 14:30 Europe/Paris

E2290 (Tours)

We consider radial solutions of fully nonlinear, uniformly elliptic equations posed in punctured balls, in presence of radial singular quadratic potentials. We discuss both the principal eigenvalues problem and the case of equations having also absorbing superlinear zero order terms: for the former problem, we  explicitly compute the principal eigenvalues, thus obtaining an extension in the fully nonlinear framework of the Hardy-Sobolev constant; for the latter case, we provide a complete classification of solutions based on their asymptotic behaviour near the singularity. The results are based on joint papers  with I. Birindelli and F. Demengel.