In this paper we deal with a class of semilinear anisotropic partial differential equations. The nonlinearity is allowed to be Gevrey of a certain order both in $x$ and $\partial^\alpha u$, with an additional condition when it is $G^{s_{\rm cr}}$ in the $(\partial^\alpha u)$-variables for a critical index $s_{\rm cr}$. For this class of equations we prove the local solvability in Gevrey classes.
Gevrey Local Solvability for Semilinear Partial Differential Equations
OLIARO, Alessandro
2002-01-01
Abstract
In this paper we deal with a class of semilinear anisotropic partial differential equations. The nonlinearity is allowed to be Gevrey of a certain order both in $x$ and $\partial^\alpha u$, with an additional condition when it is $G^{s_{\rm cr}}$ in the $(\partial^\alpha u)$-variables for a critical index $s_{\rm cr}$. For this class of equations we prove the local solvability in Gevrey classes.
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