WIAS Preprint No. 446, (1998)

Linear Elliptic Boundary Value Problems with Non-smooth Data: Normal Solvability on Sobolev-Campanato Spaces



Authors

  • Griepentrog, Jens André
  • Recke, Lutz

2010 Mathematics Subject Classification

  • 35J55 46E35 47A53

Keywords

  • 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

Abstract

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.

Appeared in

  • Math. Nachr., 225 (2001) pp. 39--74.

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