Abstract
This chapter lays the basis for our next developments. It mainly concerns the study on continuity, differentiability, and analyticity of composition operators (i.e., operators of the type \(\sigma \mapsto F(\sigma)\) where σ is an ℝN-valued function defined on Ω, and F(σ) is the real-valued function defined on Ω by setting \(F(\sigma)(x) = f(x, \sigma(x)), \forall x \in \Omega\) with \(f:\Omega \times \mathbb{R}^N \rightarrow \mathbb{R}\) a given function). Various theorems are established in Sobolev spaces and in Schauder spaces.
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© 1988 Springer-Verlag New York Inc.
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Valent, T. (1988). Composition Operators in Sobolev and Schauder Spaces. Theorems on Continuity, Differentiability, and Analyticity. In: Boundary Value Problems of Finite Elasticity. Springer Tracts in Natural Philosophy, vol 31. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3736-5_2
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DOI: https://doi.org/10.1007/978-1-4612-3736-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-8326-3
Online ISBN: 978-1-4612-3736-5
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