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. $Unknown control sequence '\hfill' 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 ɛ ⊂ ∂Ω and directed outwards Ω on ∂Ω\ɛ.

L-P-regularity for Poincare problem and applications

Palagachev, Dian Kostadinov
2005

Abstract

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. $Unknown control sequence '\hfill' 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 ɛ ⊂ ∂Ω and directed outwards Ω on ∂Ω\ɛ.
Variational Analysis and Applications
978-0-387-24209-5
Springer
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/16070
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