Abstract
Let [Formula: see text] be a lattice. For [Formula: see text], we consider the perforated space [Formula: see text] which is an [Formula: see text]-periodic open connected set with Lipschitz boundary. In [Formula: see text], we consider a self-adjoint strongly elliptic second-order differential operator [Formula: see text] with periodic coefficients depending on [Formula: see text]. We study the behavior of the resolvent [Formula: see text] for small [Formula: see text]. Approximations for this resolvent in the [Formula: see text] and [Formula: see text]-operator norms with sharp order error estimates are found. The results are obtained by the operator-theoretic (spectral) approach. General results are applied to particular periodic operators of mathematical physics: the acoustics operator, the elasticity operator, and the Schrödinger operator with a singular potential.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
