We propose a unified functional analytic approach to study the uniform analytic-Gevrey regularity and the decay of solutions to semilinear elliptic equations on R n . First, we develop a fractional calculus for nonlinear maps in Banach spaces of L p based Gevrey functions, 1< p<∞. Then we propose an abstract result on uniform analytic Gevrey regularity, which covers as particular cases solitary wave solutions to both dispersive and dissipative equations. We require a priori low H p s( R n) regularity, with s> s cr>0 depending on the nonlinearity. Next, we investigate the type of decay—polynomial or exponential—of the derivatives of solutions to semilinear elliptic equations, provided they decay a priori slowly as o(| x| − τ ), | x|→∞ for some small τ>0. The restrictions, involved in our results, are optimal. In particular, given a hyperplane L, we construct 2 d−2 strongly singular solutions (locally in H p s( R n) for s< s cr) to the semilinear Laplace equation Δ u+ cu d =0, whose singularities are concentrated on L.