Bounded Minimisers of Double Phase Variational Integrals

By Maria Colombo, Giuseppe Mingione. 2015

565 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7b514300ca01cc809f44b4a94cd995c6c2171cb9

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Lipschitz Bounds and Nonautonomous Integrals (2020, background): “As is [23, 24], we say that the p-phase occurs when (10.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, result): “We refer to the works of Baroni-Colombo-Mingione [4], [5], [6], Baroni-Kuusi-Mingione [7], CupiniMarcellini-Mascolo [16], Colombo-Mingione [14], [15], Marcellini [27], [28], Ok [33], [34], Ragusa-Tachikawa [43] and the references therein.”
Constant sign solutions for double phase problems with superlinear nonlinearity (2019, methodology): “We refer to the papers of Baroni-Colombo-Mingione [1], [2], [4], Baroni-Kussi-Mingione [3], Colombo-Mingione [6], [7] and the references therein concerning the regularity.”
Existence and multiplicity of solutions for double‐phase Robin problems (2020, background): “P. Baroni, M. Colombo and G. Mingione, ‘Harnack inequalities for double phase functionals’, Nonlinear Anal.”
Hölder regularity for nonlocal double phase equations (2019, background): “We refer to [3] and in particular to the paper [12], where it has been established the local gradient Hölder continuity of minima provided a sharp balancing condition between the closeness of p and q and the regularity of a(·) is satisfied.”
An existence result for singular Finsler double phase problems (2020, methodology): “We mention the papers of BaroniColombo-Mingione [3–5], Baroni-Kuusi-Mingione [6], Colombo-Mingione [12,13], Marcellini [32,31], Ok [35,36], Ragusa-Tachikawa [42] and the references therein.”
On double phase Kirchhoff problems with singular nonlinearity (2021, background): “4), see, for example, the works in Baroni-Colombo-Mingione [6, 7] and Colombo-Mingione [11, 12].”
Regularity for general functionals with double phase (2017, methodology): “We shall use an exit time argument, that, in a different form, has been introduced in [16, 17] to treat the regularity of minimizers of the model functional P in (1.”
Regularity for scalar integrals without structure conditions (2018, methodology): “A new impulse to the subject has been given by the recent articles already cited [11, 12, 15, 20] for the case of elliptic equations and by [6–8] for the case of parabolic equations and systems under p, q-growth.”
Hölder regularity of quasiminimizers under generalized growth conditions (2017, background): “It is interesting to note that Mingione et al. use the corresponding double phase assumption precisely when dealing bounded solutions.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “Let us mention that recently regularity theory of minimisers to variational functionals in this setting is getting increasing attention, starting from [63, 62].”