Monotonicity results for solutions of semilinear Poisson equation in epigraphs.

par Nicolas Beuvin (LAMFA, Amiens)

mardi 30 sept. 2025, 14:30 → 15:30 Europe/Paris

Fokko (ICJ)

In this talk, I am interested in the monotonicity of positives solutions to the
semilinear Poisson equation −Δu = f(u) in Ω, u = 0 in ∂Ω, where f is a globally (or locally) Lipschitz-continuous function and Ω is an epigraph
bounded from below. After presenting some existing results concerning this subject (see Berestycki-Caffarelli-Nirenberg, Esteban-Lions, · · · ), I will present new monotonicity results highlighted during my thesis. I will briefly discuss the proof which is based on the moving plane method. Finally, I will show an application of these new monotonicity results concerning the classification of non negative solutions to the semilinear Poisson equation in epigraphs bounded from below.