Seminari del Dipartimento di Matematica

Seminario del 2024

Fabiana Leoni, Sapienza Università di Roma

Radial singular solutions of fully nonlinear equations in punctured balls

nell'ambito della serie: SEMINARI DI ANALISI MATEMATICA BRUNO PINI

didattica della matematica

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 the asymptotic behavior near the singularity. The results are based on joint papers with I. Birindelli and F. Demengel.