Giulio Romani

Normalised Hamiltonian Elliptic Systems: a Gagliardo-Nirenberg inequality for bilinear mass

We study Hamiltonian elliptic systems with prescribed bilinear mass $\int_{\mathbb{R}^N}uv=a>0$. We establish a Gagliardo--Nirenberg inequality in the crossed gradient pairing and bilinear mass, on scaling-invariant component-bounded classes. It identifies the critical curve $1/p+1/q=N/(N+2)$ and the restricted energy...