The Rabinowitz continuum of subcritical Gelfand problems and free boundary-type equations arising in plasma physics.

par Daniele Bartolucci (Rome "Tor Vergata")

mardi 21 avr. 2026, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

The qualitative behavior of the Rabinowitz unbounded continuum of subcritical Gelfand problems is well known on balls in any dimension. We don't know of any such sharp and detailed description otherwise, which is our motivation to look for a new approach to the problem. The underlying idea is to describe solutions of Gelfand problems via suitably defined constrained problems of free boundary-type arising in plasma physics and to replace the usual $L^\infty$ norm of the solution with the energy of the plasma. Toward this goal, we first solve a long standing open problem of independent interest about the uniqueness of solutions of Grad-Shafranov type equations. On a ball in any dimension, we come up as expected with a bell-shaped profile of the full branch of solutions of the Gelfand problem.