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Optimality of Function Spaces in Sobolev Embeddings

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Sobolev Spaces In Mathematics I

Part of the book series: International Mathematical Series ((IMAT,volume 8))

Abstract

Abstract We study the optimality of function spaces that appear in Sobolev embeddings. We focus on rearrangement-invariant Banach function spaces. We apply methods of interpolation theory.

It is a great honor for me to contribute to this volume dedicated to the centenary of S.L. Sobolev, one of the greatest analysts of the XXth century. The paper concerns a topic belonging to an area bearing the name, called traditionally Sobolev inequalities or Sobolev embeddings. The focus will be on the sharpness or optimality of function spaces appearing in these embeddings. The results presented in this paper were established in recent years. Most of them were obtained in collaboration with Ron Kerman and Andrea Cianchi.

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Author information

Authors and Affiliations

  1. Charles University, Sokolovsk’a 83, Praha 8, Czech Republic, 186 75

    Luboš Pick

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  1. Luboš Pick
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Editors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, USA

    Vladimir Maz’ya

  2. Department of Mathematical Sciences, University of Liverpool, Liverpool, UK

    Vladimir Maz’ya

  3. Department of Mathematics, Linköping University, Linköping, Sweden

    Vladimir Maz’ya

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Pick, L. (2009). Optimality of Function Spaces in Sobolev Embeddings. In: Maz’ya, V. (eds) Sobolev Spaces In Mathematics I. International Mathematical Series, vol 8. Springer, New York, NY. https://doi.org/10.1007/978-0-387-85648-3_9

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