The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem

  • Julián Fernández BonderEmail author
  • Nicolas Saintier
  • Analía Silva


In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the existence of solutions to some critical equations involving the fractional p-Laplacian in the whole \({\mathbb {R}}^n\).


Concentration-compactness principle Unbounded domains Fractional elliptic-type problems 

Mathematics Subject Classification

35R11 46E25 45G05 



This paper was supported by Grants UBACyT 20020130100283BA, CONICET PIP 11220150100032CO and ANPCyT PICT 2012-0153. The authors are members of CONICET.


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Authors and Affiliations

  1. 1.Departamento de Matemática, Instituto de Matemática Luis Santaló, IMAS - CONICET Ciudad Universitaria, FCEyNUniversidad de Buenos AiresBuenos AiresArgentina
  2. 2.Departamento de Matemática, Ciudad Universitaria, FCEyNUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.Departamento de Matemática, Instituto de Matemática Aplicada de San Luis, IMASL, CONICET, FCFMyNUniversidad Nacional de San LuisSan LuisArgentina

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