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.
Autori: | |
Titolo: | W^{2,p}-Theory of the Poincaré Problem |
Titolo del libro: | Around the research of Vladimir Maz'ya. Vol. 3: Analysis and applications |
Editore: | Springer |
Data di pubblicazione: | 2010 |
ISBN: | 978-1-4419-1344-9 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/978-1-4419-1345-6_10 |
Appare nelle tipologie: | 2.1 Contributo in volume (Capitolo o Saggio) |
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