Nonlinear elliptic systems with general growth

By Paolo Marcellini, G. Papi. 2006

151 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/0809f8c6a0ed4fb3f8cb2b5b5d1b9bc0d069e544

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In Applied Mathematics

In Computational Theory and Mathematics

In Control and Systems Engineering

Citations in the corpus

Regularity for Double Phase Problems at Nearly Linear Growth (2023, methodology): “The functional in (1.1) appears to be a combination of the classical nearly linear growth one treated for when c ( · ) ≡ 1, as was done, for instance, in [33] and by Marcellini & Papi in [62], with a q -power growth term weighted by a non-negative coefﬁcient a ( · ) .”
Parabolic equations with p, q-growth (2013, background): “Moreover, everywhere regularity for elliptic systems of Uhlenbecktype was considered in [19,20]; in this case the vector field a in (1.”
Regularity of minimizers of autonomous convex variational integrals (2013, unknown): “[1, 2, 3, 7, 8, 9, 22, 24]).”
Higher differentiability of minimizers of convex variational integrals (2011, unknown): “[2, 4, 7, 13, 14, 33, 34]).”
Global regularity for almost minimizers of nonconvex variational problems (2008, background): “[8] and Marcellini and Papi [20] have extended Uhlenbeck’s work to allow much flexibility in the way the integrand may grow.”
Regularity of minima: An invitation to the dark side of the calculus of variations (2006, background): “Further developments can be found in [36] [241].”
A variational approach to parabolic equations under general and p,q-growth conditions (2020, background): “Among them there are variational integrands fulfilling a standard growth condition from below and above, functionals of non-standard p, q−growth and double phase (as in [4–6,23,24] and [21,29,34,35]), functionals with exponential growth (see [7,44,46]), variable exponents [21,26,33,36,37] and Orlicz”
Lipschitz estimates for systems with ellipticity conditions at infinity (2016, background): “On the other hand (see for instance [30]), we have that f (x, ξ) = g(x, |ξ |) implies fξα i (x, ξ) = gt (x, |ξ |) ξ i |ξ | fξα i ξβj (x, ξ) = ( gtt (x, |ξ |) |ξ |2 − gt (x, |ξ |) |ξ |3 ) ξ i ξ β j + gt (x, |ξ |) |ξ | δξα i ξβj .”
Lipschitz Bounds and Nonautonomous Integrals (2020, result): “The result, when combined with the approximation of Section 7 below, extends those in [57, 58, 60] to the case of nonautonomous functionals with superlinear growth as in (1.”
Existence of evolutionary variational solutions via the calculus of variations (2014, unknown): “[24,25].”
On the Regularity of Minima of Non-autonomous Functionals (2019, background): “When a(x) ≡ 0 such functionals are considered in [35, 45].”
Pointwise Calderón–Zygmund gradient estimates for the p -Laplace system (2015, background): “The papers [9, 14, 22, 28, 43, 44, 45, 47] are concerned with operators governed by general growth conditions.”
Everywhere regularity of functionals with φ-growth (2009, background): “In a recent paper [ 22 ] Marcellini and Papi proved Lipschitz regularity for local minimizers of functionals with growth conditions general enough to embrace linear and exponential ones.”
Growth conditions and regularity for weak solutions to nonlinear elliptic pdes (2020, background): “3) the integrand has exponential growth and we refer to [53], [58] and more recently to [38].”
On the Dirichlet problem for variational integrals in BV (2012, background): “for m < 3 (partially imposing the stronger bound m < ðn þ 2Þ=n; compare also Marcellini and Papi [60]).”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Amongst the very few regularity results outside spaces when a modular function is controlled by power-type functions, we shall refer to [98] for investigations on slowly growing functionals (L logL), to [155] capturing quick growth (exponential), and [156] admitting both slow and quick (but not arbi”