Uniqueness for the nonlocal Liouville equation in R
Journal of Functional Analysis(2022)
摘要
We prove uniqueness of solutions for the nonlocal Liouville equation(−Δ)1/2w=Kewin R with finite total Q-curvature ∫RKewdx<+∞. Here the prescribed Q-curvature function K=K(|x|)>0 is assumed to be a positive, symmetric-decreasing function satisfying suitable regularity and decay bounds. In particular, we obtain uniqueness of solutions in the Gaussian case with K(x)=exp(−x2).
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关键词
Liouville equation,Fractional Laplacian,Uniqueness,Nonlocal Q-curvature
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