Linear Elliptic Boundary Value Problems with Non-smooth Data: Normal Solvability on Sobolev-Campanato Spaces
- Griepentrog, Jens André
- Recke, Lutz
2010 Mathematics Subject Classification
- 35J55 46E35 47A53
- Bounded measurable coefficients, Lipschitz domains, Regular sets, Non-homogeneous mixed boundary conditions, Regularity up to the boundary of weak solutions, Smoothness of the coefficient-to-solution-map, Arbitrary space dimension
In this paper linear elliptic boundary value problems of second order with non-smooth data (L∞-coefficients, Lipschitz domains, regular sets, non-homogeneous mixed boundary conditions) are considered. It is shown that such boundary value problems generate Fredholm operators between appropriate Sobolev-Campanato spaces, that the weak solutions are Hölder continuous up to the boundary and that they depend smoothly (in the sense of a Hölder norm) on the coefficients and on the right hand sides of the equations and boundary conditions.
- Math. Nachr., 225 (2001) pp. 39--74.