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Small-energy regularity for stationary weak solutions of the Liouville equation
We establish small-energy regularity for stationary weak solutions of the Liouville equation $ -Δu=e^u $ in every dimension. It solves a problem left open in Da Lio [Commun. Partial Differ. Equations, 2008] and posed explicitly again by Da Lio and Hyder in [Commun. Contemp. Math. 2025]. The proof re
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