Abstract
Let be the elliptic complex on an n-dimensional smooth closed Riemannian manifold X with the first-order differential operators
and smooth vector bundles
over X. We consider nonlinear operator equations, associated with the parabolic differential operators
, generated by the Laplacians
of the complex
, in special Bochner–Sobolev functional spaces. We prove that under reasonable assumptions regarding the nonlinear term the Frechét derivative
of the induced nonlinear mapping is continuously invertible and the map
is open and injective in chosen spaces.
Disclosure statement
No potential conflict of interest was reported by the author(s).