Asymptotic behavior and rigidity in one-phase free boundary problems.

Abstract: In this talk, we will present some results concerning the behavior of solutions to the one-phase Bernoulli problem that are modeled –either at infinitesimal or at large scales–by one-homogeneous solutions with isolated singularity. We address the uniqueness of blow-up and blow-down limits provided that the one homogeneous solution has additional symmetries (integrability through rotations), and establish a rigidity type theorem, in the spirit of Simon-Solomon, given suitable conditions on the linearized operator around the one-homogeneous solution.

Posted on Nov 10, 2025 in Differential Equations, Seminars