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math.AP2024
Elementary Brezis-Browder type results and Representation formulae for s-harmonic functions
Damiano Greco
We prove Brezis--Browder type results for fractional Sobolev spaces and quantitative type estimates for -harmonic functions. Furthermore, we give sufficient conditions for distr…
math.AP2024
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_{…