Local solvability and hypoellipticity for semilinear anisotropic partial differential equations |
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| Authors: | Giuseppe de Donno Alessandro Oliaro |
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| Affiliation: | Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy ; Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italy |
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| Abstract: | We propose a unified approach, based on methods from microlocal analysis, for characterizing the local solvability and hypoellipticity in  and Gevrey  classes of  -variable semilinear anisotropic partial differential operators with multiple characteristics. The conditions imposed on the lower-order terms of the linear part of the operator are optimal. |
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