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Design of lattice surface energies

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Abstract

We provide a general framework for the design of surface energies on lattices. We prove sharp bounds for the homogenization of discrete systems describing mixtures of ferromagnetic interactions by constructing optimal microgeometries, and we prove a localization principle which allows to reduce to the periodic setting in the general nonperiodic case.

Mathematics Subject Classification

35B27 74Q20 82B20 49J45 49Q20 

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di Roma Tor VergataRomeItaly
  2. 2.Department of MathematicsGran Sasso Science InstituteL’AquilaItaly

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