# Holomorphic extension of solutions of semilinear elliptic equations

Research paper by Marco Cappiello, Fabio Nicola

Indexed on: 22 Apr '10Published on: 22 Apr '10Published in: Mathematics - Analysis of PDEs

#### Abstract

We prove, for a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, that the solutions which are sufficiently regular and have a certain decay at infinity extend to holomorphic functions in sectors of $\mathbb{C}^d$, improving earlier results where the extension was shown for a strip. Moreover, exponential decay for such extended solutions is also proved. The results apply, in particular, to solitary wave solutions of many classical nonlinear evolution equations.