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Nonlinear potentials and trace inequalities

  • Conference paper
The Maz’ya Anniversary Collection

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 110))

Abstract

Characterizations of trace inequalities for Sobolev spaces of the type and their generalizations are considered; here ω is a Borel measure on a domain Ω ⊂ R n, and ∇ m is the gradient of order m. A survey of the known results is presented which reflects the pioneering work of V. Maz’ya on this problem. Recent developments involving nonlinear potentials are discussed. In particular, a simple proof of the Kerman-Sawyer theorem for q = p, and a new characterization of trace inequalities for 0 < q <p, p > 1, in the case Ω = R n are given.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Missouri, Columbia, MO, 65211, USA

    I. E. Verbitsky

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  1. I. E. Verbitsky
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Rostock, D-18051, Rostock, Germany

    Jürgen Rossmann , Peter Takáč  & Günther Wildenhain ,  & 

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© 1999 Springer Basel AG

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Verbitsky, I.E. (1999). Nonlinear potentials and trace inequalities. In: Rossmann, J., Takáč, P., Wildenhain, G. (eds) The Maz’ya Anniversary Collection. Operator Theory: Advances and Applications, vol 110. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8672-7_18

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  • DOI: https://doi.org/10.1007/978-3-0348-8672-7_18

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9725-9

  • Online ISBN: 978-3-0348-8672-7

  • eBook Packages: Springer Book Archive

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