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 (INTERNATIONAL MATHEMATICAL SERIES). - In: Around the research of Vladimir Maz'ya. Vol. 3: Analysis and applications / [a cura di] Ari Laptev. - Berlin : Springer, 2010. - ISBN 978-1-4419-1344-9. - pp. 259-278 [10.1007/978-1-4419-1345-6_10]
W^{2,p}-Theory of the Poincaré Problem
PALAGACHEV, Dian Kostadinov
2010-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
