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The interior Neumann problem for the Stokes resolvent system in a bounded domain in Rn

Kohr M.

Archives of Mechanics

2007

Vol. 59, nr 3

283-304

The interior Neumann problem for the Stokes resolvent system is studied from the point of view of the potential theory. The existence and uniqueness results as well as boundary integral representations of the classical solution are given in the case of a bounded domain in Rn, having a compact but not connected boundary of class C1'" (0

On the nonlinear Neumann problem with indefinite weight and Sobolev critical nonlinearity

Chabrowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 3

323-333

We prove the existence of positive solutions of the Neumann problem with indefinite weight and critical Sobolev nonlinearity. Our approach is based on the concentration-compactness principle applied to a related variational problem.