The Singular Set of Lipschitzian Minima of Multiple Integrals
By Jan Kristensen, Giuseppe Mingione. 2007
90 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/88c25f8ccaaa14a1c8e93925e213253a7b064298
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
- Giuseppe Mingione
- Tuomo Kuusi
- Frank Duzaar
- Thomas Schmidt
- Paolo Baroni
- Verena Bogelein
- Cristiana De Filippis
- Jan Kristensen
In Computational Theory and Mathematics
- Giuseppe Mingione
- Tuomo Kuusi
- Frank Duzaar
- Thomas Schmidt
- Verena Bogelein
- Paolo Baroni
- Jan Kristensen
- Cristiana De Filippis
In Geometry and Topology
- Giuseppe Mingione
- Thomas Schmidt
- Frank Duzaar
- Tuomo Kuusi
- J. Ball
- Jan Kristensen
- Cristiana De Filippis
- Maria Colombo
Citations in the corpus
- Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth (2009, methodology): “Indeed, if f is strictly convex it can be shown by a well-known method of Giusti [26, Proposition 2.7] that the Hausdorff dimension of the singular set does not exceed n−2 and related results in the presence of x- and u-dependence have been obtained in [ 28 ].”
- New perturbation methods for nonlinear parabolic problems (2012, background): “Let us remark that asymptotic regularity results of the type just described are often crucial in establishing dimension estimates for singular sets of solutions to elliptic system (see for instance [18,19,27] and the recent survey [28] for a general overview) and in several problems coming from math”
- Progress and puzzles in nonlinear elasticity (2010, background): “For Lipschitz minimizers the Hausdorff dimension of the singular set is strictly less than n (see Kristensen & Mingione [23]).”
- Regularity of minima: An invitation to the dark side of the calculus of variations (2006, result): “Under additional assumptions, either on the structure of the integrand F , or on the regularity of the minimizer u, a few, first results, have been obtained by Kristensen & myself in [207].”
- Harmonic type approximation lemmas (2009, background): “Starting by the basic paper of Evans [36], there is a nowadays rather developed partial regularity theory for minimizers of quasiconvex functionals; see [3,14] for optimal statements, and [58] for the first results concerning the Hausdorff dimension of the singular sets.”