 |
||||||||
| Volume 7, Number 3, December 2006, pp. 499-513 | ||||||||
|
Dian K. Palagachev
|
||||||||
| Key words: | ||||||||
| Uniformly elliptic operator, Poincaré problem, Neutral vector field, Strong solution, a priori estimates, Lp-Sobolev spaces. | ||||||||
| Mathematices Subject Classification: Primary: 35J25, 35R25; Secondary: 35B45, 35R05, 35H20 | ||||||||
|
||||||||||||||||||||||||||||||||||||||||
| Abstract: | |||
| A degenerate oblique derivative problem is studied for uniformly elliptic operators with low regular coefficients in the framework of Sobolev's classes W2;p(Ω) for arbitrary p > 1: The boundary operator is prescribed in terms of a directional derivative with respect to the vector field ℓ that becomes tangential to αΩ at the points of some non-empty subset ε ⊂ αΩ and is directed outwards Ω on αΩ ∖ ε: Under quite general assumptions of the behaviour of ℓ; we derive a priori estimates for the W2;p(Ω) -strong solutions for any p ∈ (1,∞): | |||
| W2,p-a priori estimates for the neutral Poincaré problem | ||