A new approach to variational problems with multiple scales

By Giovanni S. Alberti, Stefan Müller. 2001

107 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/992a4fabe36478eb784d2c695372db79722141c0

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In Applied Mathematics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Uniform energy distribution for an isoperimetric problem with long-range interactions (2008, unknown): “[1, 17, 22, 4, 29]).”
Vanishing viscosity limit of the Navier‐Stokes equations to the euler equations for compressible fluid flow (2009, unknown): “Following Alberti-Müller [1] (also see Ball [2] and Tartar [31]), we find that, given any sequence of measurable functions (ρε ,uε) : R(2)+ → H̄ , there exists a subsequence (still labeled (ρε ,uε)) and a function νt,x ∈ L∞ w ( R(2)+; Prob(H̄ ) )”
2D Coulomb Gases and the Renormalized Energy (2012, methodology): “imit of wn was ν = limn ~un. In taking the Γ-limit of Fn, the limiting object is more complex, it is the limit P of Pνn, i.e. a Young measure akin to the Young measures on micropatterns introduced in [AM]. Note that in the rest of the paper, the probability P has nothing to do with Pβn, and depends ”
Droplet Minimizers of an Isoperimetric Problem with Long‐Range Interactions (2011, background): “, the one of the phase separation and that of the pattern formation) could force the Γ-limit to be defined on more complex spaces of Young measures as it happens in the one dimensional case addressed by Alberti and Müller [3].”
Asymptotic expansions by Γ-convergence (2008, methodology): “The equivalence of the two problems in some regimes can be deduced from [1,53,58].”
Transport equation and Cauchy problem for BV vector fields (2004, background): “2 of [ 4 ]; in functional analytic terms it can be derived from the duality (L 1 (A; C(K ))) ∗ = L ∞ (A; (C(K )) ∗ ).”
From the Ginzburg-Landau Model to Vortex Lattice Problems (2010, methodology): “of a good subset of Lp loc. We must restrict to a compact subset of L p loc(R 2,R2) in a suitable way. This is not surprising when constructing an approximation: note that the set of micropatterns in [AM] is assumed to be compact, and we need to reduce to this case. This is the aim of the following ”