Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4590550 | Journal of Functional Analysis | 2014 | 30 Pages |
Abstract
We show that to each symmetric elliptic operator of the formA=âââkaklâl+c on a bounded Lipschitz domain ΩâRd one can associate a self-adjoint Dirichlet-to-Neumann operator on L2(âΩ), which may be multi-valued if 0 is in the Dirichlet spectrum of A. To overcome the lack of coerciveness in this case, we employ a new version of the Lax-Milgram lemma based on an indirect ellipticity property that we call hidden compactness. We then establish uniform resolvent convergence of a sequence of Dirichlet-to-Neumann operators whenever the underlying coefficients converge uniformly and the second-order limit operator in L2(Ω) has the unique continuation property. We also consider semigroup convergence.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
W. Arendt, A.F.M. ter Elst, J.B. Kennedy, M. Sauter,