Regularity of minima: An invitation to the dark side of the calculus of variations

By Giuseppe Mingione. 2006

462 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/e922818ca916a73df3b4917dc2d88ef1ab2c0275

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In Applied Mathematics

In Computational Mechanics

In Computational Theory and Mathematics

Citations in the corpus

Boundary Regularity in Variational Problems (2010, background): “By now standard references on partial regularity include [25, 23, 20, 2, 18, 31, 45, 46, 50, 51]; an up-dated presentation is in [42].”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, background): “The mathematical literature on the regularity under p, q growth is very large; it is now well known that a restriction between p and q must be imposed since the counterexamples in [20,24–26]; we refer to [32] for a complete survey on the subject.”
Harnack inequalities for double phase functionals (2015, background): “Now, while in the case of an autonomous energy density of the type F (x,w,Dw) ≡ F (Dw) the regularity theory of minima of functionals with (p, q)-growth conditions is by now well-understood (see for instance [4, 5, 27, 13, 24, 29]), the case of non-autonomous integrals is still very much open and in”
Regularity of minimizers under limit growth conditions (2017, unknown): “The bibliography on the regularity under p, q-growth is large; we recall some recent papers on the subject: [2,7,6,21] and, by the authors, [9,12]; in the vector-valued case [10,11]; we refer to [26] for a detailed survey on the subject.”
Besov spaces with variable smoothness and integrability (2010, methodology): “For an overview we refer to the surveys [14, 21, 30, 36] and the monograph [13].”
Gradient estimates for elliptic equations with Lp(·)logL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^{p(\cdot )}\ (2016, background): “They are not only the mathematical generalization of a standard p-growth condition, but also motivated by various applications fields such as homogenization of strongly anisotropic materials, electrorheological fluids, image processing models and so on, see the survey paper [28].”
Overview of differential equations with non-standard growth (2010, background): “Mingione [156] has written an extensive exposition of regularity theory, including the non-standard growth case; Fan [84] summarized some results of his research group on the existence and multiplicity of solutions of eigenvalue problems.”
n-Harmonic Mappings Between Annuli (2011, methodology): “We appeal to the C 1,α-regularity theory of n-harmonic mappings [13, 36, 47, 48, 49].”
On the Regularity of Minima of Non-autonomous Functionals (2019, background): “3), see for instance [3, 4, 11, 12, 14, 16–22, 48, 51] and [46, 49] for overviews.”
Regularity for scalar integrals without structure conditions (2018, result): “The mathematical literature on the regularity under p, q-growth is now very large; we refer to [32–35] and to [36] for a complete survey on the subject.”
Regularity for general functionals with double phase (2017, background): “als have been the object of intensive investigation over the last years, starting with the seminal papers of Marcellini [43, 44, 45]; see for instance [9, 11, 15, 26, 55, 57, 58]. See also the survey [46]. The regularity theory in the case of functionals with (p,q)-growth in the non-autonomous case,”
The boundary regularity of non-linear parabolic systems I (2010, methodology): “Results of this type have been obtained in the stationary case both for systems [16,31–33] and variational integrals [27–29] but are still missing in the parabolic case.”
Regularity results for vectorial minimizers of a class of degenerate convex integrals (2018, background): “Actually, the research in this field is so intense that it is almost impossible to give an exhaustive and comprehensive list of references; we confine ourselves to refer the interested reader to the survey [39] and the more recent papers [1], [8], [9] and the references therein.”