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• W2003054669 abstract "We study a degenerate oblique derivative problem for linear uniformly elliptic operators with low regular coefficients within the framework of the Sobolev spaces W 2,p (Ω) with arbitrary p > 1. The boundary operator is prescribed in terms of a directional derivative with respect to a vector field ℓ that becomes tangent to ∂ Ω at the points of a non-empty set ℰ ⊂ ∂ Ω and is of emergent type on ∂Ω. We extend the results from Palagachev (2005 Palagachev , D. K. ( 2005 ). The Poincaré problem in L p -Sobolev spaces I: codimension one degeneracy . J. Funct. Anal. 229 : 121 – 142 .[Crossref] , [Google Scholar]) regarding a priori estimates, strong solvability, uniqueness and Fredholmness of the problem under consideration to the general case of arbitrary set of tangency ℰ which may have positive surface measure." @default.
• W2003054669 created "2016-06-24" @default.
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• W2003054669 date "2008-01-31" @default.
• W2003054669 modified "2023-09-27" @default.
• W2003054669 title "The Poincaré Problem in<i>L</i>^<i>p</i>-Sobolev Spaces II: Full Dimension Degeneracy" @default.
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• W2003054669 doi "https://doi.org/10.1080/03605300701454933" @default.
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