Differentiation, implicit functions, and applications to generalized well-posedness
Seppo I Hiltunen
Abstract
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f:E sqcap F to F which can be lifted to Keller Ckpi maps fi:E sqcap Fi to Fi with Fi Banach and F=projlim Fi . We prove theorems about existence and differentiability of functions g satisfying f(x,g(x))=b constant. In addition to these abstract theorems, we give several examples of applications to proving smooth dependence of the solution on initial/boundary values and the nonlinearity in nonlinear (partial) differential equations.
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