We study the local nonsolvability for several classes of partial differential equations and systems in Gevrey $G^s$, $s>1$ and Schwartz distribution spaces. The principal symbol is a power of Mizohata type operator or sum of squares of Mizohata type operators. In particular, for a square of locally solvable Mizohata operator with analytic coefficients, the sufficiently small order of vanishing of the lower order term at $0$ guarantees the local nonsolvability in each $G^s$ space with $s$ large enough.
Local solvability for partial differential equations with multiple characteristics
OLIARO, Alessandro;RODINO, Luigi Giacomo
2004-01-01
Abstract
We study the local nonsolvability for several classes of partial differential equations and systems in Gevrey $G^s$, $s>1$ and Schwartz distribution spaces. The principal symbol is a power of Mizohata type operator or sum of squares of Mizohata type operators. In particular, for a square of locally solvable Mizohata operator with analytic coefficients, the sufficiently small order of vanishing of the lower order term at $0$ guarantees the local nonsolvability in each $G^s$ space with $s$ large enough.
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