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 c r >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 2d-2 strongly singular solutions (locally in H p s (R n ) for s<s c r ) to the semilinear Laplace equation Δu+cu d =0, whose singularities are concentrated on L.