Gamma-Convergence for Beginners

By Andrea Braides. 2002

561 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/347cb1067830d20105aba5f4b5cffb71a2585f1d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Martin Burger
2. Stanley J. Osher
3. Carola-Bibiane Schönlieb
4. Gabriele Steidl
5. Tanja Teuber
6. Lénaïc Chizat
7. Bernhard Schmitzer
8. Akihiro Takezawa

In Computational Theory and Mathematics

1. Carola-Bibiane Schönlieb
2. Houssam Abdoul-Anziz
3. G. Peyr'e
4. J. D. L. Reyes
5. Martin Burger
6. Gabriele Steidl
7. Stanley J. Osher
8. Akihiro Takezawa

In Mechanics of Materials

1. Houssam Abdoul-Anziz
2. Martin Burger
3. Gabriele Steidl
4. Carola-Bibiane Schönlieb
5. Stanley J. Osher
6. Akihiro Takezawa
7. Tanja Teuber
8. Pierre Seppecher

Citations in the corpus

• Removing Multiplicative Noise by Douglas-Rachford Splitting Methods (2010, background): “By the (cid:13) -convergence (16) and since the functionals T ϕ,k and T ψ,k are equi-coercive it follows that T ϕ,k ( ˆ w k ) → T ϕ ( ˆ w) and T ψ,k (g k ( ˆ w k )) → T ϕ ( ˆ u) and that each cluster point of { ˆ w k } k is ˆ w and of { g k ( ˆ w k ) } k is ˆ u , see [8, p. 29].”
• Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, methodology): “…of the slender substructures: we have then identified the effective energy through a (cid:48) - convergence theorem (for a simple definition of this notion the reader can refer to [Braides 2002] or [Dal Maso 1993]) using tools of double scale convergence (see [Nguetseng 1989] or [Allaire 1992]).”
• A survey on level set methods for inverse problems and optimal design (2005, background): “As → 0 and α( ) → 0, this relaxation converges to the original shape optimization problem under appropriate conditions on J̃ in the sense of Γ -convergence [43, 21].”
• The structure of optimal parameters for image restoration problems (2015, background): “Our assumption (33) says that the family {Iγ′, ′ | (γ′, ′) ∈ [γ̄, ∞] × [0, ̄ ]} is equi-mildly coercive in the sense of [9].”
• Shape and topology optimization based on the phase field method and sensitivity analysis (2010, background): “Mathematical details and proofs can be found in [54, 55].”
• Unbalanced optimal transport: Dynamic and Kantorovich formulations (2015, background): “Here we give the corresponding result for the static problems in terms of Γ -convergence [5].”