The Singular Set of ω-minima

By Jan Kristensen, Giuseppe Mingione. 2005

65 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/6419958d649bdbf8953cb3d7f302d26c8abe6631

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Gradient potential estimates (2011, unknown): “We shall revisit some techniques of [22, 23, 27].”
Global regularity for almost minimizers of nonconvex variational problems (2008, background): “The first statement in the next lemma follows from the convexity of f , property (U)v, and the previous lemma (see [19] or [23], for example).”
Regularity for Double Phase Problems at Nearly Linear Growth (2023, methodology): “Notice that inequalities (5.36) are obtained via a dyadic/atomic decomposition technique, ﬁnding its roots in [52], that resembles the one used for Besov spaces [2,67] ), but no matter how small the exponent α 0 is.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “For the previous result, which improves in certain cases the one in [204], I refer to the forthcoming paper [208], to which I also refer to for results in the case of functionals (2.”
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.”
Harmonic type approximation lemmas (2009, background): “1) we have that the Hausdorff dimension of Σu is strictly less than n− 2, while for estimates in more general cases we refer to [67,68,57,56,70] and related references.”
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007, background): “These intervene in many contexts when dealing with regularity problems in the Calculus of Variations [20,8,13,23].”
Boundary Regularity in Variational Problems (2010, methodology): “Here we exploit in a more subtle way the interaction, already identified in [40, 41, 34, 36], between the higher integrability of the gradient and singular sets estimates.”
Gradient estimates below the duality exponent (2010, result): “In contrast to those from the previous sections, the results in this one rely on the methods introduced in [53] - see also [42] and [43] - where Theorem”