We present some recent results regarding the W 2,p -theory of a degenerate oblique derivative problem for second order uniformly elliptic operators. The boundary operator is prescribed in terms of directional derivative with respect to a vector field l which is tangent to ¶W at the points of a nonempty set e Ì ¶W : Sufficient conditions are given ensuring existence, uniqueness and regularity of solutions in the L p-Sobolev scales. Moreover, we show that the problem considered is of Fredholm type with index zero.

W^{2,p}-Theory of the Poincaré Problem

PALAGACHEV, Dian Kostadinov
2010

Abstract

We present some recent results regarding the W 2,p -theory of a degenerate oblique derivative problem for second order uniformly elliptic operators. The boundary operator is prescribed in terms of directional derivative with respect to a vector field l which is tangent to ¶W at the points of a nonempty set e Ì ¶W : Sufficient conditions are given ensuring existence, uniqueness and regularity of solutions in the L p-Sobolev scales. Moreover, we show that the problem considered is of Fredholm type with index zero.
Around the research of Vladimir Maz'ya. Vol. 3: Analysis and applications
978-1-4419-1344-9
Springer
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/12511
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