Regularity results for a class of quasiconvex functionals with nonstandard growth

By E. Acerbi, Giuseppe Mingione. 2001

109 citations recorded by the source corpus.

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Citations in the corpus

Regularity of solutions to a class of variable–exponent fully nonlinear elliptic equations (2018, background): “The case of systems is the subject of [3].”
Regularity Results for a Class of Functionals with Non-Standard Growth (2001, background): “whose solutions correspond to minimizers of F when µ = 0. In this last case p(x) also appears as an unknown of the system itself, and this eventually leads us to look for minimal regularity assumptions on it. Leaving to a forthcoming paper [ 5 ] the analysis of the vector-valued case N> 1, we restri”
Overview of differential equations with non-standard growth (2010, background): “u ∈ W 1,p(·)(Ω,RN ), N > 2, see [27], stating that the result could be extended to the case F = F (x, u,∇u).”
Regularity of Relaxed Minimizers of Quasiconvex Variational Integrals with (p, q)-growth (2009, result): “Moreover, our regularity theory should be compared to the results of [6] in the setting of p(x)-growth conditions.”
Regularity of minimizers of W1,p-quasiconvex variational integrals with (p,q)-growth (2008, background): “Note that another regularity result for quasiconvex integrals under nonstandard growth conditions, namely p(x)-growth conditions, has been established in [ 4 ].”
Partial Regularity for BV Minimizers (2018, methodology): “Partial regularity in the general subquadratic case was established by CAROZZA, FUSCO & MINGIONE in [19], and many interesting extensions have followed since then, including [2, 3, 21, 34, 36, 23, 26, 28, 27, 47, 48, 70].”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “4) and/or suitable reinforcements [5, 6, 7, 8, 66].”
Partial regularity of $p(x)$-harmonic maps (2011, background): “Among the many related papers in the literature, in a noncomprehensive way, we recall the study made by Acerbi and Mingione in [1], by Fan and Zhao in [10] and later in [11].”