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math.AP2026
Normalised Hamiltonian Elliptic Systems: a Gagliardo-Nirenberg inequality for bilinear mass
Daniele Cassani, Giulio Romani
We study Hamiltonian elliptic systems with prescribed bilinear mass . We establish a Gagliardo--Nirenberg inequality in the crossed gradient pairing and…
math.AP2026
Mixed-dispersion Schrödinger equations and Gagliardo-Nirenberg inequalities: equivalence between ground states and optimizers
Zhisu Liu, Giulio Romani, Yu Su
We study a nonlinear Schrödinger equation with mixed dispersion in the mass competition regime, namely mass-supercritical for the Laplacian and mass-subcritical for the Bilaplacian…
math.AP2026
A blow-up approach for a priori bounds in semilinear planar elliptic systems: the Brezis-Merle critical case
Laura Baldelli, Gabriele Mancini, Giulio Romani
We establish uniform a priori estimates for solutions of semilinear planar Hamiltonian elliptic systems in a ball with Dirichlet boundary conditions. We consider a broad class of c…