We consider semilinear equations $p(x,D)u=F[u]$, where the linear parts $p(x,D)$ are pseudo\-differential operators of Shubin type, with symbols satisfying a global ellipticity condition in $\R^{n}.$ For classical solutions $u \in H^{s}(\R^{n}), s >n/2,$ we obtain properties of super-exponential decay and holomorphic extension, expressed in terms of Gelfand-Shilov classes.
Exponential estimates and holomorphic extensions for semilinear elliptic pseudodifferential equations
CAPPIELLO, Marco;RODINO, Luigi Giacomo
2011-01-01
Abstract
We consider semilinear equations $p(x,D)u=F[u]$, where the linear parts $p(x,D)$ are pseudo\-differential operators of Shubin type, with symbols satisfying a global ellipticity condition in $\R^{n}.$ For classical solutions $u \in H^{s}(\R^{n}), s >n/2,$ we obtain properties of super-exponential decay and holomorphic extension, expressed in terms of Gelfand-Shilov classes.
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