Superposition of functions in Sobolev spaces of fractional order. A survey

a contrastive study of rhetorical functions of citation in iranian and international elt scopus journals

writing an academic article requires the researchers to provide support for their works by learning how to cite the works of others. various studies regarding the analysis of citation in m.a theses have been done, while little work has been done on comparison of citations among elt scopus journal articles, and so the dearth of research in this area demands for further investigation into citatio...

Composition operators acting on Sobolev spaces of fractional order – a survey on sufficient and necessary conditions

What follows is a survey of recent results on sufficient and necessary conditions on composition operators to map one Sobolev space of fractional order into another. This report may be taken as a continuation of the contribution of G.Bourdaud given at the forerunner conference of this one, held in Friedrichroda 1992, cf. [Bo 5]. Composition operators are simple examples of nonlinear operators. ...

Composition Operators Acting on Sobolev Spaces of Fractional Order { a Survey on Suucient and Necessary Conditions

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چکیده ندارد.

Superposition with subunitary powers in Sobolev spaces

Let 0 < a < 1 and set Φ(t) = |t|, ∀ t ∈ R. Let 1 < p < ∞ and n ≥ 1. We prove that the superposition operator u 7→ Φ(u) maps the Sobolev space W (R) into the fractional Sobolev space W (R). We also investigate the case of more general nonlinearities. Résumé. Superposition avec des puissances sousunitaires dans les espaces de Sobolev. Pour 0 < a < 1, soit Φ(t) = |t|, ∀ t ∈ R. Soient 1 < p < ∞ et ...