. FA ] 1 9 A ug 2 00 5 Differentiation , implicit functions , and applications to generalized well - posedness by Seppo Hiltunen
نویسنده
چکیده
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f : E⊓F → F which can be lifted to Keller C π –maps fi : E ⊓ Fi → Fi with Fi Banach and F = proj limFi . 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.
منابع مشابه
m at h . FA ] 1 2 A ug 2 00 5 Differentiation , implicit functions , and applications to generalized well - posedness
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f : E⊓F → F which can be lifted to Keller C π –maps fi : E ⊓ Fi → Fi with Fi Banach and F = proj limFi . 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 examp...
متن کامل. FA ] 1 3 A pr 2 00 5 Differentiation , implicit functions , and applications to generalized well - posedness
This article is centered around generalizing a previous implicit function theorem of the author to be applicable for maps f : E⊓F → F which can be lifted to Keller C π –maps fi : E ⊓ Fi → Fi with Fi Banach and F = proj limFi . 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 examp...
متن کامل0 v 1 [ m at h . FA ] 1 8 M ay 2 00 5 On the definition of some Banach spaces over bounded domains with irregular boundary by
This note aims to clarify the interrelations of certain inequivalently defined Banach spaces denoted by C (Ω) for a natural number i and a bounded open set Ω. We give some sufficient conditions for the equality of these spaces, and present examples to show that the spaces indeed can be unequal for Ω having irregular boundary.
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متن کاملN ov 2 00 5 On the definition of some Banach spaces over bounded domains with irregular boundary by Seppo Hiltunen
This note aims to clarify the interrelations of certain inequivalently defined Banach spaces denoted by C (Ω) for a natural number i and a bounded open set Ω. We give some sufficient conditions for the equality of these spaces, and present examples to show that the spaces indeed can be unequal for Ω having irregular boundary.
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