Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider a class of evolution operators with real-analytic coefficients and study their local solvability both in $L^2$ as well as in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg--Treves condition $(\psi)$ which is suitable to our study.
Local Solvability for a Class of Evolution Equations
PERNAZZA, LUDOVICO
2010-01-01
Abstract
Motivated by the celebrated example of Y. Kannai of a linear partial differential operator which is hypoelliptic but not locally solvable, we consider a class of evolution operators with real-analytic coefficients and study their local solvability both in $L^2$ as well as in the weak sense. In order to do so we are led to propose a generalization of the Nirenberg--Treves condition $(\psi)$ which is suitable to our study.File in questo prodotto:
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