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 (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS). - In: Variational Analysis and Applications / [a cura di] Franco Giannessi; Antonino Maugeri. - STAMPA. - Boston, MA : Springer, 2005. - ISBN 978-0-387-24209-5. - pp. 773-789 [10.1007/0-387-24276-7_46]
L-P-regularity for Poincare problem and applications
Palagachev, Dian Kostadinov
2005-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
