Microlocal Regularity for Mizohata Type Differential Operators

Abstract

<jats:p>We investigate interesting connections between Mizohata type vector fields and microlocal regularity of nonlinear first-order PDEs, establishing results in Denjoy–Carleman classes and real analyticity results in the linear case.</jats:p>

On local solvability for a class of generalized Mizohata equations

“…We mention that, using this notion as proposed by us, G. Hoepfner and R. Medrado, in [9], proved propagation of singularities for this class of operators, in the Gevrey's category.…”