We prove sharp analytic estimates and holomorphic extensions in sectors of $\C^{d}$ for the solutions of a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, improving earlier results where the extension was shown for a strip. Moreover, we derive exponential decay estimates for such extended solutions. The results presented apply in particular to solitary wave solutions of many classical nonlinear evolution equations as KdV-type, long-wave type and Schrodinger equations.

Holomorphic extension of solutions of semilinear elliptic equations

CAPPIELLO, Marco;
2011-01-01

Abstract

We prove sharp analytic estimates and holomorphic extensions in sectors of $\C^{d}$ for the solutions of a wide class of semilinear elliptic differential and pseudodifferential equations in $\R^d$, improving earlier results where the extension was shown for a strip. Moreover, we derive exponential decay estimates for such extended solutions. The results presented apply in particular to solitary wave solutions of many classical nonlinear evolution equations as KdV-type, long-wave type and Schrodinger equations.
2011
74
2663
2681
Semilinear elliptic equations; holomorphic extension; solitary waves; exponential decay; ground states.
M. Cappiello; F. Nicola
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/84661
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