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math.AP2025
Smoothness and stability in the Alt-Phillips problem
Matteo Carducci, Giorgio Tortone
We study the one-phase Alt-Phillips free boundary problem, focusing on the case of negative exponents . The goal of this paper is twofold. On the one hand, we prove sm…
math.AP2025
Free boundary regularity for a tumor growth model with obstacle
Giulia Bevilacqua, Matteo Carducci
We develop an existence and regularity theory for solutions to a geometric free boundary problem motivated by models of tumor growth. In this setting, the tumor invades an accessib…
math.AP2025
Existence and regularity in the fully nonlinear one-phase free boundary problem
Matteo Carducci, Bozhidar Velichkov
We consider viscosity solution to one-phase free boundary problems for general fully nonlinear operators and free boundary condition depending on the normal vector. We show existen…