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Solvability for semilinear PDE with multiple characteristics

Alessandro OliaroLuigi Rodino — 2003

Banach Center Publications

We prove local solvability in Gevrey spaces for a class of semilinear partial differential equations. The linear part admits characteristics of multiplicity k ≥ 2 and data are fixed in G σ , 1 < σ < k/(k-1). The nonlinearity, containing derivatives of lower order, is assumed of class G σ with respect to all variables.

Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity

Giuseppe De DonnoAlessandro Oliaro — 2006

Bollettino dell'Unione Matematica Italiana

We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in C and Gevrey G λ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension n 3 . The conditions for our results are imposed on the sign of the lower order terms of the linear part of the operator, see Theorem 1.1 and Theorem 1.3 below.

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