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W 2,p-Theory of the Poincaré Problem

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Book cover Around the Research of Vladimir Maz'ya III

Part of the book series: International Mathematical Series ((IMAT,volume 13))

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Abstract

We present some recent results regarding the W 2,p-theory of a degenerate oblique derivative problem for second order uniformly elliptic operators. The boundary operator is prescribed in terms of directional derivative with respect to a vector field l which is tangent to \(\partial \Omega \) at the points of a nonempty set \(\varepsilon \subset \partial \Omega \): Sufficient conditions are given ensuring existence, uniqueness and regularity of solutions in the L p-Sobolev scales. Moreover, we show that the problem considered is of Fredholm type with index zero.

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Authors and Affiliations

  1. Department of Mathematics, Technical University of Bari, Via E. Orabona 4, 70125, Bari, Italy

    Dian K. Palagachev

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  1. Dian K. Palagachev
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Correspondence to Dian K. Palagachev .

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  1. Department of Mathematics, Imperial College, Queen's Gate 180, London, SW7 2AZ, United Kingdom

    Ari Laptev

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Palagachev, D.K. (2010). W 2,p-Theory of the Poincaré Problem. In: Laptev, A. (eds) Around the Research of Vladimir Maz'ya III. International Mathematical Series, vol 13. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-1345-6_10

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