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,W-p(Omega) 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 partial derivative Omega at the points of a non-empty set E subset of partial derivative Omega and is of emergent type on partial derivative Omega. We extend the results from Palagachev (2005) 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.

The Poincaré Problem in L p -Sobolev Spaces II: Full Dimension Degeneracy / Palagachev, Dian Kostadinov. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 33:2(2008), pp. 209-234. [10.1080/03605300701454933]

The Poincaré Problem in L p -Sobolev Spaces II: Full Dimension Degeneracy

Palagachev, Dian Kostadinov
2008-01-01

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,W-p(Omega) 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 partial derivative Omega at the points of a non-empty set E subset of partial derivative Omega and is of emergent type on partial derivative Omega. We extend the results from Palagachev (2005) 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.
2008
The Poincaré Problem in L p -Sobolev Spaces II: Full Dimension Degeneracy / Palagachev, Dian Kostadinov. - In: COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0360-5302. - STAMPA. - 33:2(2008), pp. 209-234. [10.1080/03605300701454933]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/9481
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