ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

10. Partial Differential Equations

1991 MS Classification: 35J65 Ebmeyer, Carsten, Universität Bonn, Germany The p-Laplacian under mixed boundary value conditions in multidimensional polyhedral domains. The equation −div(|∇u|^{p−2}∇u) = f is considered on a bounded polyhedral domain Ω ⊂ IR^{n}, where n ≥ 3. Mixed Dirichlet-Neumann boundary conditions are given. Thus, the solution u may have singularities on the boundary. Using a difference quotient technique, we prove that u ∈ W^{s,p}(Ω) for s < \frac{3}{2}. This generalizes the known results for the case when p = 2. Reference: C. Ebmeyer and J. Frehse, Mixed boundary value problems for nonlinear equations in multidimensional non-smooth domains, (to appear).