Relaxation of convex functionals: the gap problem

By E. Acerbi, G. Bouchitté, Irene Fonseca. 2003

49 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/00a10b358cb7757929efe4f1af0c47058dcf23d9

How researchers see this paper

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

In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Regularity for Double Phase Problems at Nearly Linear Growth (2023, background): “For more related results on the absence of Lavrentiev phenomenon we refer to the recent papers [1, 3, 4, 16, 50, 51] and related references.”
Non-autonomous functionals, borderline cases and related function classes (2016, background): “Functionals with (p, q) occur in several problems from elasticity and mathematical materials science; they have been studied at length in the setting of relaxation and lower semicontinuity; see for instance [1, 32, 39].”
Bounded Minimisers of Double Phase Variational Integrals (2015, background): “Conditions of this type are also known to play an important role in semicontinuity problems, see [1],[25],[32].”
Higher differentiability of minimizers of convex variational integrals (2011, background): “Let F : RN×n → R be an integrand satisfying the assumptions (H1), (H2) with q < p + 1 and μ ∈ [0, 1], where 2 ≤ p < n.”
Regularity for Double Phase Variational Problems (2015, background): “Similar difficulties occur in relaxation and semicontinuity problems for integral functionals (see for instance [1], [23], [34] and in particular [16, Remark 5.”
On the Regularity of Minima of Non-autonomous Functionals (2019, background): “dx, where λ ∈ [0, 1] and Fk(t) ≈ tLk(1 + t) , {”
Recent developments in problems with nonstandard growth and nonuniform ellipticity (2021, background): “See also [1,37,103,109] for connections with relaxed functionals and more examples.”
Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “In [1] it is proved that the singular part of the measure representation of relaxed integrals with p(x)-growth fades out if and only if A4 holds true.”