Sharp regularity for functionals with (p,q) growth

By L. Esposito, Francesco Leonetti, Giuseppe Mingione. 2004

384 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/69a8c08da92dd324a8e05fa8a14952210ede64d8

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Regularity of minimizers of vectorial integrals with p − q growth (2003, background): “Firstly studied by Marcellini [14], various contributions to the subject have been provided in these last years, see [4,15,16] for an extensive list of references.”
A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “The optimal closeness condition in the case of a Hölder continuous weight a ∈ C obtained in [88] requires q/p ≤ 1 + α/N .”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, neutral): “We mention the papers of Baroni-Colombo-Mingione [4, 5, 6], Baroni-Kuusi-Mingione [7], Byun-Oh [9, 10], Byun-Youn [11], Colombo-Mingione [14, 15, 16], De Filippis-Mingione [18, 19, 20], De Filippis-Palatucci [21], EspositoLeonetti-Mingione [23], Esposito-Leonetti-Petricca [24], Marcellini [37, 38, 3”
Fully anisotropic elliptic problems with minimally integrable data (2019, background): “They are the topic of diverse contributions, including [17,18,35,41,46,57,61].”
Hölder regularity for nonlocal double phase equations (2019, background): “6] and also the related preliminary result for what concerns the analysis of the Lavrentiev effect in [18].”
Harnack inequalities for double phase functionals (2015, methodology): “For the functional Pp,q a very sharp interaction occurs between the size of the phase transition, measured by the distance between p and q, and the regularity of the coefficient a(·), as initially shown in [14, 16].”
New Examples on Lavrentiev Gap Using Fractals (2019, methodology): “This example was generalized by Esposito, Leonetti and Mingione in [8] to the case of higher dimensions and less regular weights, i.”
Regularity for general functionals with double phase (2017, methodology): “See for instance the lists of examples discussed in [6, 26, 56, 57, 58].”
Lipschitz Bounds and Nonautonomous Integrals (2020, methodology): “oblems one typically recovers classical theories as Schauder’s [54] and Calderón-Zygmund’s [12]. This is in general not the case for the double phase integral in (1.10), due to the counterexamples in [37,39]. Nevertheless the integrand H(·) turns out to be uniformly elliptic when using the quantity ”