LP-Regularity for Poincaré Problem and Applications

  • Dian K. Palagachev
Part of the Nonconvex Optimization and Its Applications book series (NOIA, volume 79)


We improve the results from [10] on strong solvability and uniqueness for the oblique derivative problem
$$ \left\{ \begin{gathered} a^{ij} \left( x \right)D_{ij} u + b^i \left( x \right)D_i u + c\left( x \right)u = f\left( x \right) a.a. in \Omega , \hfill \\ \partial u/\partial \ell + \sigma \left( x \right)u = \varphi \left( x \right) on \partial \Omega , \hfill \\ \end{gathered} \right. $$
extending them to Sobolev’s space W 2,p (Ω), for any p > 1. The vector field ℓ(x) tangent to Ω at the points of ɛΩ and directed outwards Ω on Ω\ɛ.

Key words

Uniformly elliptic operator Poincaré problem Strong solutions 


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Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Dian K. Palagachev
    • 1
  1. 1.Dept. of MathematicsTechnical University of BariBariItaly

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