Linear elliptic boundary value problems with non-smooth data: Normal solvability on Sobolev-Campanato spaces. (English) Zbl 1009.35019

Griepentrog, Jens A.; Recke, Lutz

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

Summary: Linear elliptic boundary value problems of second order with non-smooth data (\(L^\infty\)-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.

MSC:

35J25	Boundary value problems for second-order elliptic equations
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35J55	Systems of elliptic equations, boundary value problems (MSC2000)
47A53	(Semi-) Fredholm operators; index theories

Keywords:

\(L^\infty\)-coefficients; Lipschitz domains; regular sets; nonhomogeneous mixed boundary conditions; regularity up to the boundary of weak solutions; smoothness of the coefficient-to-solution-map; arbitrary space dimension

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