D. Borisov, I. Nakić, C. Rose, M. Tautenhahn, Ivan Veselić: Multiscale unique continuation properties of eigenfunctions

Author(s):

D. Borisov
I. Nakić
C. Rose
M. Tautenhahn
Ivan Veselić

Title:

D. Borisov, I. Nakić, C. Rose, M. Tautenhahn, Ivan Veselić: Multiscale unique continuation properties of eigenfunctions

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 14, 2014

Mathematics Subject Classification:

    35R45 []
    35-06 []
    35A23 []

Abstract:

Quantitative unique continuation principles for multiscale structures are an important ingredient in a number applications, e.g.\ random Schr\"odinger operators and control theory. We review recent results and announce new ones regarding quantitative unique continuation principles for partial differential equations with an underlying multiscale structure. They concern Schr\"odinger and second order elliptic operators. An important feature is that the estimates are scale free and with quantitative dependence on parameters. These unique continuation principles apply to functions satisfying certain "rigidity" conditions, namely that they are solutions of the corresponding elliptic equations, or projections on spectral subspaces. Carleman estimates play an important role in the proofs of these results.

Keywords:

Language:

English

Publication time:

09/2014