Y.A.Alkhutov and V.V.Zhikov, Existence theorems for solutions of parabolic equations with variable order of nonlinearity, Proc Steklov Inst Math.270 (2010), 15–26. doi:10.1134/S0081543810030028.
2.
Y.A.Alkhutov and V.V.Zhikov, Hölder continuity of solutions of parabolic equations with variable nonlinearity exponent, J Math Sci (N. Y.)179(3) (2011), 347–389. doi:10.1007/s10958-011-0599-9.
3.
Y.A.Alkhutov and V.V.Zhikov, Existence and uniqueness theorems for solutions of parabolic equations with a variable nonlinearity exponent, Sb Math.205(3) (2014), 307–318. doi:10.1070/SM2014v205n03ABEH004377.
4.
S.Bonafede and I.I.Skrypnik, On Hölder continuity of solutions of doubly nonlinear parabolic equations with weight, Ukrainian Math J.51(7) (1999), 996–1012. doi:10.1007/BF02592036.
5.
E.DiBenedetto, Degenerate Parabolic Equations, Springer, New York, 1993.
6.
E.DiBenedetto, U.Gianazza and V.V.Alternative, Forms of the Harnack inequality for non-negative solutions to certain degenerate and singular parabolic equations, Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl.20 (2009), 369–377. doi:10.4171/RLM/552.
7.
E.DiBenedetto, U.Gianazza and V.V.Forward, Backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial differential equations, Ann Scuola Norm Sup Pisa Cl Sci (5)IX (2010), 385–422.
8.
E.DiBenedetto, U.Gianazza and V.V.Harnack, Estimates for quasi-linear degenerate parabolic differential equation, Acta Math.200 (2008), 181–209. doi:10.1007/s11511-008-0026-3.
9.
E.DiBenedetto, U.Gianazza and V.Vespri, Local clustering of the non-zero set of functions in , Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei (9) Mat Appl.17 (2006), 223–225. doi:10.4171/RLM/465.
10.
E.DiBenedetto, U.Gianazza and V.Vespri, Harnack’s Inequality for Degenerate and Singular Parabolic Equations, Springer, New York, 2012.
11.
L.Diening, P.Harjulehto, P.Hästö and R.M.Lebesgue, Sobolev Spaces with Variable Exponents, Lecture Notes in Mathematics, Vol. 2017, Springer, Berlin, 2011.
12.
L.Diening, P.Nägele and M.Růz˘hic˘ka, Monotone operator theory for unsteady problems in variable exponent spaces, Complex Var Elliptic Equ.57(11) (2012), 1209–1231. doi:10.1080/17476933.2011.557157.
13.
T.Kuusi, Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations, Ann Scuola Norm Sup Pisa Cl Sci (5)7(4) (2008), 673–716.
14.
O.A.Ladyzhenskaya, V.A.Solonnikov and N.N.Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, Vol. 23, AMS, Providence (RI), 1967.
15.
O.A.Ladyzhenskaya and N.N.Uraltseva, Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968.
16.
I.I.Skrypnik, Regularity of solutions of degenerate quasilinear parabolic equations (weighted case), Ukrainian Math J.48(7) (1996), 1099–1118. doi:10.1007/BF02390967.
17.
I.I.Skrypnik and M.V.Voitovych, classes of De Giorgi–Ladyzhenskaya–Ural’tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions, Nonlinear Anal.202 (2021), 112135. doi:10.1016/j.na.2020.112135.
18.
I.I.Skrypnik and M.V.Voitovych, On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions, Ann Mat Pura Appl. (2021). doi:10.1007/s10231-021-01161-y.
19.
M.Surnachev, A Harnack inequality for weighted degenerate parabolic equations, J Differential Equations248 (2010), 2092–2129. doi:10.1016/j.jde.2009.08.021.
20.
M.D.Surnachev, Regularity of solutions of parabolic equations with a double nonlinearity and a weight, Trans. Moscow Math. Soc.75 (2014), 259–280. doi:10.1090/S0077-1554-2014-00237-5.
21.
Y.Wang, Intrinsic Harnack inequalities for parabolic equations with variable exponents, Nonlinear Anal.83 (2013), 12–30. doi:10.1016/j.na.2013.01.010.
22.
V.V.Zhikov, On Lavrentiev’s phenomenon, Russian J. Math. Phys.3(2) (1995), 249–269.
23.
V.V.Zhikov, On variational problems and nonlinear elliptic equations with nonstandard growth conditions, J Math Sci (N. Y.)173(5) (2011), 463–570. doi:10.1007/s10958-011-0260-7.
