Ground states of a nonlocal variational problem and Thomas-Fermi limit for the Choquard equation

Damiano Greco, Yanghong Huang, Zeng Liu +1

We study nonnegative optimizers of a Gagliardo-Nirenberg type inequality $$\iint_{\mathbb{R}^N \times \mathbb{R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-α}} dx\, dy\le C\Big(\int_{…