Fractional derivative estimates in Gevrey spaces, global regularity and decay for solutions to semilinear equations in

We propose a unified functional analytic approach to study the uniform analytic-Gevrey regularity and the decay of solutions to semilinear elliptic equations on . First, we develop a fractional calculus for nonlinear maps in Banach spaces of Lp based Gevrey functions, 1scr>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 for s