The Singular Set of Minima of Integral Functionals

By Jan Kristensen, Giuseppe Mingione. 2006

208 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4704a117f39a8ff15712429dd69930d9b122f9d6

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Bounded Minimisers of Double Phase Variational Integrals (2015, background): “3 (Calderón-Zygmund estimate [33]).”
Boundary Regularity in Variational Problems (2010, background): “In fact full boundary regularity follows in such cases, a result that is known to fail in the general vectorial case (see [23]).”
The existence of regular boundary points for non-linear elliptic systems (2007, methodology): “However, the proofs in [35] apply essentially unchanged in the sub-quadratic too, see also [2], Lemma 2.”
Hitchhiker's guide to the fractional Sobolev spaces (2011, background): “equations, are now experiencing impressive applications in different subjects, such as, among others, the thin obstacle problem [87, 69], optimization [37], finance [26], phase transitions [2, 14, 88, 40, 45], stratified materials [83, 23, 24], anomalous diffusion [68, 98, 65], crystal dislocation [”
Gradient estimates below the duality exponent (2010, background): “Specifically, starting from some arguments developed in [20],[43],[1] in different contexts, the level sets of the Hardy-Littlewood maximal function of |Du| are seen to be locally controlled by the level sets of a suitable Riesz potential operator, namely I1(|f |).”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, unknown): “The first results in this direction can be found in my papers [248] [249], that I will summarize now, also keeping into account of some later improvements in [206] [98].”
The Calderón-Zygmund theory for elliptic problems with measure data (2006, methodology): “We shall use a delicate combination of some the arguments from the latter paper with the Morrey space estimates of Section 8, a direct comparison argument on certain Calderón-Zygmund type balls, and finally a modification of some ideas from [14, 48].”
Parabolic systems with polynomial growth and regularity (2011, methodology): “We remark that, unlike in the elliptic case [44, 28, 52], no use of Harmonic Analysis tools is made here, and no use can actually be made due to the occurrence in the estimates of the intrinsic cylinders, in turn ruling out the possibility of use of maximal operators.”
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007, methodology): “For Lipschitzian solutions this improves the results in [23,24] for minimizers of convex integrands when the Hölder exponent α is small.”
Gradient regularity for elliptic equations in the Heisenberg group (2007, methodology): “Indeed, these will allow for a suitable application of recent non-linear techniques for obtaining higher integrability estimates for non-homogeneous equations [5, 35].”
Partial Hölder continuity for discontinuous elliptic problems with VMO‐coefficients (2011, background): “Results related to the work of Foss and Mingione [9] were also obtained at the boundary for a Dirichlet boundary condition by Beck [1] and for problems with a non-standard growth condition of p(x)-type by Habermann [17].”
Higher differentiability of minimizers of convex variational integrals (2011, methodology): “We refer the interested reader to [1, 13, 24, 25, 26, 28, 38, 39] and the references therein.”