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Uniqueness and nondegeneracy for Dirichlet fractional problems in bounded domains via asymptotic methods
Abdelrazek Dieb, Isabella Ianni, Alberto Saldaña
We consider positive solutions of a fractional Lane-Emden type problem in a bounded domain with Dirichlet conditions. We show that uniqueness and nondegeneracy hold for the asympto…
Prescribed Gauss curvature problem on singular surfaces
Teresa D'Aprile, Francesca De Marchis, Isabella Ianni
We study the existence of at least one conformal metric of prescribed Gaussian curvature on a closed surface admitting conical singularities of orders 's at points 's…
Asymptotic profile of positive solutions of Lane-Emden problems in dimension two
Francesca De Marchis, Isabella Ianni, Filomena Pacella
We consider families of solutions to the problem \begin{equation}\label{problemAbstract} \left\{\begin{array}{lr}-Δu= u^p & \mbox{ in }Ω\\ u>0 & \mbox{ in }Ω\\ u=0 & \mbox{ o…
Blow-up for sign-changing solutions of the critical heat equation in domains with a small hole
I. Ianni, M. Musso, A. Pistoia
We consider the critical heat equation \begin{equation} \label{CH}\tag{CH} \begin{array}{lr} v_t-Δv =|v|^{\frac{4}{n-2}}v & Ω_ε\times (0, +\infty) \\ v=0 & \partialΩ_ε\times (0, +\…