Global regularity for almost minimizers of nonconvex variational problems

By Mikil Foss. 2008

75 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/9b92eb018e721dab89f0abb34a9e185b67dfed0f

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Boundary Regularity in Variational Problems (2010, unknown): “Some of the results presented here can be manipulated in order to cover a certain number of model problems which where not treated before and that in view of the recent literature devoted to the subject [10, 15, 21, 47], could have their own interest.”
Global Boundedness of the Gradient for a Class of Nonlinear Elliptic Systems (2012, background): “Further contributions on gradient regularity up to the boundary for systems and variational problems with Uhlenbeck structure, or perturbations of it, are [2,24,25].”
Asymptotically regular problems I: Higher integrability (2010, background): “6) for some p ≥ 2 (see also [51,26,27,21,24]).”
The Singular Set of Lipschitzian Minima of Multiple Integrals (2007, methodology): “For such global regularity results, as well as for their validity in the case of ω-minima we refer to recent paper by Foss [15].”
Global Calderón–Zygmund theory for nonlinear parabolic systems (2013, methodology): “Global Morrey and Lipschitz regularity re-sults have been obtained by Foss [24] and Foss & Passarelli di Napoli & Verde [25].”
Asymptotically regular problems II: Partial Lipschitz continuity and a singular set of positive measure (2009, background): “Moreover, various related results (see for instance [10, 13–15, 20, 29, 34]) have by now been established and we refer the reader to the first part [36] of this work for an extensive discussion of such issues and further references.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “A striking example of LP for functionals with variable growth exponent (see the last section) has been offered by Foss [127]; LP also play an important role in non-linear elasticity, see [25, 130, 131].”
New perturbation methods for nonlinear parabolic problems (2012, background): “Asymptotic regularity We start with the missing parabolic version of certain classical elliptic results which have been extensively developed over the last years; see for instance [7,32,11,12,24,33] and related references.”
Regularity for Double Phase Variational Problems (2015, background): “We notice that functional appearing in the above display has standard polynomial growth of order 2q−p, therefore by standard regularity theory (see for instance [18], [25]) we know that vm ∈W 1,∞ loc (B1) .”