Regularity for double phase problems under additional integrability assumptions

By Jihoon Ok. 2020

71 citations recorded by the source corpus.

Abstract We study the regularity of quasi-minimizers or minimizers of functionals of double phase type. In recent years, Baroni, Colombo and Mingione have investigated regularity theory for bounded minimizers in Baroni et al. (2015, 2018); Colombo and Mingione (2015) . In this paper, we assume the minimizers only belong to L γ -space.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/689d06f4268a51d0e732ed6f74c64b49c22b8bd1

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

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.”
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.”
A new class of double phase variable exponent problems: Existence and uniqueness (2021, methodology): “We refer to the works of Baroni-Colombo-Mingione [6, 7, 8], Baroni-Kuusi-Mingione [9], Byun-Oh [16], Colombo-Mingione [20, 21], De Filippis [22], De Filippis-Palatucci [24], Harjulehto-Hästö-Toivanen [42], Marcellini [51, 52], Ok [54, 55], 2020 Mathematics Subject Classification.”
Sign changing solution for a double phase problem with nonlinear boundary condition via the Nehari manifold (2020, unknown): “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.”
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”