Every nontrivial nonnegative finite-energy weak solution of the doubly critical quasilinear Hartree equation with Hardy potential is radially symmetric and strictly decreasing, with sharp power-law asymptotics at the origin and infinity.
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Radial symmetry and sharp asymptotic behaviors of nonnegative solutions to weighted doubly $D^{1,p}$-critical quasi-linear nonlocal elliptic equations with Hardy potential
Every nontrivial nonnegative finite-energy weak solution of the doubly critical quasilinear Hartree equation with Hardy potential is radially symmetric and strictly decreasing, with sharp power-law asymptotics at the origin and infinity.