An existence result for a nonconvex variational problem via regularity

By Irene Fonseca, N. Fusco, Paolo Marcellini. 2002

92 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/4ab588a550e933165cf90e82965cb7e8e34dc6a5

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Congested traffic dynamics, weak flows and very degenerate elliptic equations (2010, methodology): “5 L∞ estimates for the gradient The proof of the Lipschitz regularity result will easily follow from results of Fonseca-Fusco-Marcellini [15] that we now recall (under slightly stronger assumptions which will be sufficient for our purpose).”
Regularity results for vectorial minimizers of a class of degenerate convex integrals (2018, background): “Under these assumptions it has been proven that the minimizers of the functional F are locally Lipschitz continuous (see for example [19], [22], [24], [25], [26], [44]).”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, background): “Now we proceed in a similar way as in [9,16].”
Continuity in two dimensions for a very degenerate elliptic equation (2009, background): “boundedness of ∇u, we mention [8], which uses these estimates for existence purposes, and [7], which improves the regularity results.”
Regularity results for very degenerate elliptic equations (2014, background): “Hence, since |∇uε| ≤M , we obtain that, up to adding a constant a subsequence, uε → u0 uniformly in Ω′ and (5.17) ∇uε ⇀ ∇u0 weakly∗ in L∞(Ω′) for some Lipschitz function u0.”
Regularity for scalar integrals without structure conditions (2018, background): “In this context see [10, 14, 25] and recently [13, 19, 20].”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “I shall start presenting an innovative result by Fonseca & Fusco [122] [123] [110], concerning integral functionals of the type (2.12) G s (v) := loc (Ω, R n ).”
On certain anisotropic elliptic equations arising in congested optimal transport: Local gradient bounds (2014, background): “1As shown in [14], in general the upper bound on D(2)F is not really necessary and can be replaced by a growth assumption on ∇F .”