Regularity results for generalized double phase functionals

By Sun-Sig Byun, Jehan Oh. 2020

96 citations recorded by the source corpus.

We consider a wide class of functionals with the property of changing their growth and ellipticity properties according to the modulating coefficients in the framework of Musielak–Orlicz spaces. In particular, we provide an optimal condition on the modulating coefficient to establish the Holder regularity and Harnack inequality for quasiminimizers of the generalized double phase functional with (G,H)-growth for two Young functions G and H.

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

View Paper: https://www.semanticscholar.org/paper/d48f6526801a0ddc902ff1438554c352f0a2e1cf

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

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”
Hölder regularity for weak solutions to nonlocal double phase problems (2021, background): “5) and minimizers of corresponding variational integral has been exhaustively studied, see [2, 4, 11, 14, 15, 37] and references therein.”
Regularity for Double Phase Problems at Nearly Linear Growth (2023, background): “These also include integrals of the type where t (cid:2)→ Φ 1 ( t ) has superlinear growth (these have been treated in [6,17]).”
Existence of solutions for singular double phase problems via the Nehari manifold method (2021, unknown): “We mention the papers of Baroni–Colombo–Mingione [4–6], Baroni–Kuusi–Mingione [7], Byun– Oh [9, 10], Byun–Youn [11], Colombo–Mingione [14–16], De Filippis–Mingione [18–20], De Filippis–Palatucci [21], Esposito–Leonetti–Mingione [23], Esposito– Leonetti–Petricca [24],Marcellini [37–39], Ok [44, 45], ”