[1] Bahrouni, A., Rădulescu, V. D., Repovš, D. D.: Double phase transonic flow problems with variable growth: Nonlinear patterns and stationary waves. Nonlinearity 32 (2019), 2481-2495. DOI 10.1088/1361-6544/ab0b03 | MR 3957220 | Zbl 1419.35056

[2] Baroni, P., Colombo, M., Mingione, G.: Harnack inequalities for double phase functionals. Nonlinear Anal., Theory Methods Appl., Ser. A 121 (2015), 206-222. DOI 10.1016/j.na.2014.11.001 | MR 3348922 | Zbl 1321.49059

[3] Baroni, P., Colombo, M., Mingione, G.: Non-autonomous functionals, borderline cases and related function classes. St. Petersbg. Math. J. 27 (2016), 347-379. DOI 10.1090/spmj/1392 | MR 3570955 | Zbl 1335.49057

[4] Baroni, P., Colombo, M., Mingione, G.: Regularity for general functionals with double phase. Calc. Var. Partial Differ. Equ. 57 (2018), Article ID 62, 48 pages. DOI 10.1007/s00526-018-1332-z | MR 3775180 | Zbl 1394.49034

[5] Byun, S.-S., Oh, J.: Regularity results for generalized double phase functionals. Anal. PDE 13 (2020), 1269-1300. DOI 10.2140/apde.2020.13.1269 | MR 4149062 | Zbl 1477.49057

[6] Colombo, M., Mingione, G.: Bounded minimisers of double phase variational integrals. Arch. Ration. Mech. Anal. 218 (2015), 219-273. DOI 10.1007/s00205-015-0859-9 | MR 3360738 | Zbl 1325.49042

[7] Colombo, M., Mingione, G.: Regularity for double phase variational problems. Arch. Ration. Mech. Anal. 215 (2015), 443-496. DOI 10.1007/s00205-014-0785-2 | MR 3294408 | Zbl 1322.49065

[8] Cupini, G., Marcellini, P., Mascolo, E.: Local boundedness of minimizers with limit growth conditions. J. Optim. Theory Appl. 166 (2015), 1-22. DOI 10.1007/s10957-015-0722-z | MR 3366102 | Zbl 1325.49043

[9] Filippis, C. De, Oh, J.: Regularity for multi-phase variational problems. J. Differ. Equations 267 (2019), 1631-1670. DOI 10.1016/j.jde.2019.02.015 | MR 3945612 | Zbl 1422.49037

[10] Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics 2017. Springer, Berlin (2011). DOI 10.1007/978-3-642-18363-8 | MR 2790542 | Zbl 1222.46002

[11] Esposito, L., Leonetti, F., Mingione, G.: Sharp regularity for functionals with $(p,q)$ growth. J. Differ. Equations 204 (2004), 5-55. DOI 10.1016/j.jde.2003.11.007 | MR 2076158 | Zbl 1072.49024

[12] Fan, X., Zhao, D.: On the spaces $L^{p(x)}$ and $W^{m,p(x)}(\Omega)$. J. Math. Anal. Appl. 263 (2001), 424-446. DOI 10.1006/jmaa.2000.7617 | MR 1866056 | Zbl 1028.46041

[13] Fonseca, I., Malý, J., Mingione, G.: Scalar minimizers with fractal singular sets. Arch. Ration. Mech. Anal. 172 (2004), 295-307. DOI 10.1007/s00205-003-0301-6 | MR 2058167 | Zbl 1049.49015

[14] Gilbarg, D., Trudinger, N. S.: Elliptic Partial Differential Equations of Second Order. Classics in Mathematics. Springer, Berlin (2001). DOI 10.1007/978-3-642-61798-0 | MR 1814364 | Zbl 1042.35002

[15] Giusti, E.: Direct Methods in the Calculus of Variations. World Scientific, Singapore (2003). DOI 10.1142/5002 | MR 1962933 | Zbl 1028.49001

[16] Harjulehto, P., Hästö, P.: Double phase image restoration. J. Math. Anal. Appl. 501 (2021), Article ID 123832, 12 pages. DOI 10.1016/j.jmaa.2019.123832 | MR 4258782 | Zbl 1472.49026

[17] Harjulehto, P., Hästö, P., Toivanen, O.: Hölder regularity of quasiminimizers under generalized growth conditions. Calc. Var. Partial Differ. Equ. 56 (2017), Article ID 22, 26 pages. DOI 10.1007/s00526-017-1114-z | MR 3606780 | Zbl 1366.35036

[18] Kim, S., Ri, D.: Global boundedness and Hölder continuity of quasiminimizers with the general nonstandard growth conditions. Nonlinear Anal., Theory Methods Appl., Ser. A 185 (2019), 170-192. DOI 10.1016/j.na.2019.02.016 | MR 3926581 | Zbl 1419.49045

[19] Kováčik, O., Rákosník, J.: On spaces $L^{p(x)}$ and $W^{k,p(x)}$. Czech. Math. J. 41 (1991), 592-618. DOI 10.21136/CMJ.1991.102493 | MR 1134951 | Zbl 0784.46029

[20] Ladyzhenskaya, O. A., Ural'tseva, N. N.: Linear and Quasilinear Elliptic Equations. Nauka, Moskva (1973), Russian. MR 0509265 | Zbl 0269.35029

[21] Leonetti, F., Petricca, P. V.: Regularity for minimizers of integrals with nonstandard growth. Nonlinear Anal., Theory Methods Appl., Ser. A 129 (2015), 258-264. DOI 10.1016/j.na.2015.09.009 | MR 3414930 | Zbl 1327.49064

[22] Lieberman, G. M.: The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Commun. Partial Differ. Equations 16 (1991), 311-361. DOI 10.1080/03605309108820761 | MR 1104103 | Zbl 0742.35028

[23] Marcellini, P.: Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions. Arch. Ration. Mech. Anal. 105 (1989), 267-284. DOI 10.1007/BF00251503 | MR 0969900 | Zbl 0667.49032

[24] Marcellini, P.: Regularity and existence of solutions of elliptic equations with $p,q$-growth conditions. J. Differ. Equations 90 (1991), 1-30. DOI 10.1016/0022-0396(91)90158-6 | MR 1094446 | Zbl 0724.35043

[25] Rădulescu, V. D.: Isotropic and anisotropic double-phase problems: Old and new. Opusc. Math. 39 (2019), 259-279. DOI 10.7494/OpMath.2019.39.2.259 | MR 3897817 | Zbl 1437.35315

[26] Ragusa, M. A., Tachikawa, A.: Regularity for minimizers for functionals of double phase with variable exponents. Adv. Nonlinear Anal. 9 (2020), 710-728. DOI 10.1515/anona-2020-0022 | MR 3985000 | Zbl 1420.35145

[27] Yu, C., Ri, D.: Global $L^{\infty}$-estimates and Hölder continuity of weak solutions to elliptic equations with the general nonstandard growth conditions. Nonlinear Anal., Theory Methods Appl., Ser. A 156 (2017), 144-166. DOI 10.1016/j.na.2017.02.019 | MR 3634773 | Zbl 1375.35127

[28] Zhikov, V. V.: Averaging of functionals of the calculus of variations and elasticity theory. Math. USSR, Izv. 29 (1987), 33-66. DOI 10.1070/IM1987v029n01ABEH000958 | MR 0864171 | Zbl 0599.49031

[29] Zhikov, V. V.: On Lavrentiev's phenomenon. Russ. J. Math. Phys. 3 (1995), 249-269. MR 1350506 | Zbl 0910.49020