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Grand Sobolev spaces and their applications in geometric function theory and PDEs

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Function spaces that are slightly larger than the Lebesgue L p(Ω) spaces (even larger than the Marcinkiewicz L p,∞(Ω) spaces) have been introduced by Iwaniec and Sbordone [Arch. Ration. Mech. Anal. 119 (1992), 129–143] in connection with integrability properties of the Jacobian. These are the grand Lebesgue spaces L p)(Ω). In this survey we collect a number of results which prove that these spaces are useful in various classical settings of geometric function theory and partial differential equations (PDEs).

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Authors and Affiliations

  1. Università “Parthenope”, Via Parisi 13, 80100, Napoli, Italy

    Luigi D’Onofrio

  2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Via Cintia, 80126, Napoli, Italy

    Carlo Sbordone & Roberta Schiattarella

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  1. Luigi D’Onofrio
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  2. Carlo Sbordone
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  3. Roberta Schiattarella
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Correspondence to Carlo Sbordone.

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D’Onofrio, L., Sbordone, C. & Schiattarella, R. Grand Sobolev spaces and their applications in geometric function theory and PDEs. J. Fixed Point Theory Appl. 13, 309–340 (2013). https://doi.org/10.1007/s11784-013-0140-5

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