Harnack inequalities for double phase functionals

By Paolo Baroni, Maria Colombo, Giuseppe Mingione. 2015

397 citations recorded by the source corpus.

We prove a Harnack inequality for minimisers of a class of non-autonomous functionals with non-standard growth conditions. They are characterised by the fact that their energy density switches between two types of different degenerate phases.

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

View Paper: https://www.semanticscholar.org/paper/60c6e9ee3283f077b9847b30fdadc98ae9db4d2c

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Extrapolation and interpolation in generalized Orlicz spaces (2018, background): “When φ(x, t) = t we get the variable Lebesgue spaces which have been extensively studied in the past 25 years [18, 24, 33], and when φ(x, t) = t + a(x)t, p < q, we get the double phase functional recently studied in [5, 13].”
On the Regularity of Minima of Non-autonomous Functionals (2019, neutral): “3), see for instance [3, 4, 11, 12, 14, 16–22, 48, 51] and [46, 49] for overviews.”
A borderline case of Calder\'on-Zygmund estimates for non-uniformly elliptic problems (2019, background): “In [2, 4, 9, 10] the authors have provided a basic regularity theory for minimizers of double phase functionals of the type P(v,Ω) := ∫”
The maximal operator on generalized Orlicz spaces (2015, methodology): “[18] regarding the optimality); (3) The double phase functional φ(x, t) = t + a(x)t of Mingione and collaborators [1, 2, 3], where the sharp condition for the regularity of minimizers is recovered, namely q p < 1 + α n with a ∈ C (Theorem 4.”
Existence of solutions for double phase obstacle problems with multivalued convection term (2020, neutral): “We refer to Baroni-Colombo-Mingione [3], [4], [5], Baroni-Kussi-Mingione [6], Colombo-Mingione [10], [11], CupiniMarcellini-Mascolo [12] and Marcellini [21], [22] and the references therein.”
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems (2022, methodology): “In this direction we mention the works of Baroni-ColomboMingione [5, 6, 7], Baroni-Kuusi-Mingione [8], Byun-Oh [12], Colombo-Mingione [17, 18], De Filippis [19], De Filippis-Palatucci [26], Harjulehto-Hästö-Toivanen [38], Marcellini [51, 52], Ok [58, 59], Ragusa-Tachikawa [62, 63] and the references”
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].”