Journal of Global Optimization

, Volume 40, Issue 1, pp 305–318

W2,p-a priori estimates for the emergent Poincaré Problem


DOI: 10.1007/s10898-007-9175-8

Cite this article as:
Palagachev, D.K. J Glob Optim (2008) 40: 305. doi:10.1007/s10898-007-9175-8


We derive W2,p(Ω)-a priori estimates with arbitrary p ∈(1, ∞), for the solutions of a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular coefficients. The boundary operator is given in terms of directional derivative with respect to a vector field ℓ that is tangent to ∂Ω at the points of a non-empty set ε ⊂ ∂Ω and is of emergent type on ∂Ω.


Uniformly elliptic operator Poincaré problem Emergent vector field Strong solution A priori estimates Lp-Sobolev spaces 

Mathematics Subject Classification (2000)

Primary: 35J25 35R25 Secondary: 35R05 35B45 35H20 58J32 

Copyright information

© Springer Science+Business Media LLC 2007

Authors and Affiliations

  1. 1.Dipartimento di MatematicaPolitecnico di BariBariItaly

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