Homogenization of quadratic convolution energies in periodically perforated domains
-
Andrea Braides
and
Andrey Piatnitski
Abstract
We prove a homogenization theorem for quadratic convolution energies defined in perforated domains. The corresponding limit is a Dirichlet-type quadratic energy, whose integrand is defined by a non-local cell-problem formula. The proof relies on an extension theorem from perforated domains belonging to a wide class containing compact periodic perforations.
Funding source: Ministero dell’Istruzione, dell’Universitá e della Ricerca
Award Identifier / Grant number: E83C18000100006
Funding statement: The authors acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.
References
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Articles in the same Issue
- Frontmatter
- Michell truss type theories as a Γ-limit of optimal design in linear elasticity
- The local structure of the free boundary in the fractional obstacle problem
- Homogenization of quadratic convolution energies in periodically perforated domains
- Uniqueness and nonuniqueness of limits of Teichmüller harmonic map flow
- Regularity for minimizers of a class of non-autonomous functionals with sub-quadratic growth
- On a comparison principle for Trudinger’s equation
- Equivalence of ray monotonicity properties and classification of optimal transport maps for strictly convex norms
- An extensive study of the regularity of solutions to doubly singular equations
- New features of the first eigenvalue on negatively curved spaces
- High order curvature flows of plane curves with generalised Neumann boundary conditions
- (BV,L p )-decomposition, p = 1,2, of functions in metric random walk spaces
- Causal variational principles in the σ-locally compact setting: Existence of minimizers
- On sub-Riemannian geodesic curvature in dimension three
- Existence for singular critical exponential (𝑝, 𝑄) equations in the Heisenberg group
