Holomorphic extension of solutions of semilinear elliptic equations

Details Holomorphic extension of solutions of semilinear elliptic equations Holomorphic extension of solutions of semilinear elliptic equations

2010-04-22

arxiv.org/abs/1004.3885v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

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.

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