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Advances in Nonlinear Analysis

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Uniform continuity and Brézis–Lieb-type splitting for superposition operators in Sobolev space

Nils Ackermann
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  • Instituto de Matemáticas, Universidad Nacional Autónoma de México, Circuito Exterior, C.U., 04510 México D.F., Mexico
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Published Online: 2016-10-11 | DOI: https://doi.org/10.1515/anona-2016-0123


Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker assumptions on the nonlinearity than known before. An intermediate result on the uniform continuity of superposition operators in Sobolev space is of independent interest.

Keywords: Superposition operator; Sobolev space; uniform continuity; Brézis–Lieb splitting

MSC 2010: 47H30; 58E40


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About the article

Received: 2016-06-02

Revised: 2016-08-15

Accepted: 2016-08-16

Published Online: 2016-10-11

Published in Print: 2018-11-01

Funding Source: Consejo Nacional de Ciencia y Tecnología

Award identifier / Grant number: 237661

Funding Source: Dirección General de Asuntos del Personal Académico, Universidad Nacional Autónoma de México

Award identifier / Grant number: IN104315

This research was partially supported by CONACYT grant 237661 and UNAM-DGAPA-PAPIIT grant IN104315 (Mexico).

Citation Information: Advances in Nonlinear Analysis, Volume 7, Issue 4, Pages 587–599, ISSN (Online) 2191-950X, ISSN (Print) 2191-9496, DOI: https://doi.org/10.1515/anona-2016-0123.

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