On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity
Yu. A. Alkhutov, O. V. Krasheninnikova

This publication is cited in the following articles:

1. O. V. Hadzhy, M. O. Savchenko, I. I. Skrypnik, “On asymptotic behavior of solutions to non-uniformly elliptic equations with generalized Orlicz growth: to the memory of Mykhailo Voitovych”, J Elliptic Parabol Equ, 2025  
2. Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack inequality for solutions of the p(x)-Laplace equation under the precise non-logarithmic Zhikov's conditions”, Calc. Var., 63:1 (2024)  
3. Tran Thi Hanh, Cong Nhan Le, “A New De Giorgi class type related to the Caffarelli-Kohn-Nirenberg weights and Hölder continuity”, Journal of Mathematical Analysis and Applications, 2024, 128696  
4. Mokhtar Naceri, “Variable exponents anisotropic nonlinear elliptic systems with Lp′→(⋅)-data”, Applicable Analysis, 2024, 1  
5. Andrii S. Bychkov, Oleksandr V. Hadzhy, Yevhen S. Zozulia, “On the generalized weak Harnack inequality for non-negative super-solutions of quasilinear elliptic equations with absorption term”, J Math Sci, 282:1 (2024), 13  
6. Simone Ciani, Eurica Henriques, Igor I. Skrypnik, “The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth”, Advances in Calculus of Variations, 2024  
7. Andrii S. Bychkov, Oleksandr V. Hadzhy, Yevhen S. Zozulia, “On the generalized weak Harnack inequality for non-negative super-solutions of quasilinear elliptic equations with absorption term”, UMB, 21:1 (2024), 16  
8. Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition”, J Math Sci, 273:3 (2023), 427  
9. Ihor Skrypnik, Maria Savchenko, Yevgeniia Yevgenieva, “Weak Harnack inequality for unbounded solutions to the p(x)-Laplace equation under the precise non-logarithmic conditions”, Proc. IAMM NASU, 37 (2023), 48  
10. Mariia Savchenko, Igor Skrypnik, Yevgeniia Yevgenieva, “Harnack's inequality for degenerate double phase parabolic equations under the non-logarithmic Zhikov's condition”, UMB, 20:1 (2023), 124  
11. Skrypnik I.I., Voitovych M.V., “On the Continuity of Solutions of Quasilinear Parabolic Equations With Generalized Orlicz Growth Under Non-Logarithmic Conditions”, Ann. Mat. Pura Appl., 201:3 (2022), 1381–1416      
12. Yu. A. Alkhutov, M. D. Surnachev, “A Variation on the p(x)-Laplace Equation”, J Math Sci, 268:3 (2022), 266  
13. Igor I. Skrypnik, “Harnack's inequality for singular parabolic equations with generalized Orlicz growth under the non-logarithmic Zhikov's condition”, J. Evol. Equ., 22:2 (2022)  
14. Skrypnik I.I., Voitovych M.V., “B-1 Classes of de Giorgi-Ladyzhenskaya-Ural'Tseva and Their Applications to Elliptic and Parabolic Equations With Generalized Orlicz Growth Conditions”, Nonlinear Anal.-Theory Methods Appl., 202 (2021), 112135      
15. Shan M.A., Skrypnik I.I., Voitovych M.V., “Harnack'S Inequality For Quasilinear Elliptic Equations With Generalized Orlicz Growth”, Electron. J. Differ. Equ., 2021    
16. Maria A. Shan, Igor I. Skrypnik, Mykhailo V. Voitovych, “Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth”, ejde, 2021:01-104 (2021), 27  
17. Yu. A. Alkhutov, M. D. Surnachev, “Interior and boundary continuity of $p(x)$-harmonic functions”, J. Math. Sci. (N. Y.), 283:5 (2024), 699–720    
18. Yu. A. Alkhutov, M. D. Surnachev, “Hölder Continuity and Harnack's Inequality for $p(x)$-Harmonic Functions”, Proc. Steklov Inst. Math., 308 (2020), 1–21            
19. Yu. A. Alkhutov, M. D. Surnachev, “Harnack inequality for the elliptic $p(x)$-Laplacian with a three-phase exponent $p(x)$”, Comput. Math. Math. Phys., 60:8 (2020), 1284–1293          
20. Igor I. Skrypnik, Mykhailo V. Voitovych, “$ {\mathfrak{B}}_1 $ classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth”, J Math Sci, 246:1 (2020), 75  
21. Yu. A. Alkhutov, M. D. Surnachev, “Harnack's inequality for the $p(x)$-Laplacian with a two-phase exponent $p(x)$”, J. Math. Sci. (N. Y.), 244:2 (2020), 116–147      
22. Igor Skrypnik, Mykhailo Voitovych, “\mathfrak{B}_{1} classes of De Giorgi, Ladyzhenskaya, and Ural'tseva and their application to elliptic and parabolic equations with nonstandard growth”, UMB, 16:3 (2019), 403  
23. M. D. Surnachev, “O neravenstve Kharnaka dlya $p(x)$-laplasiana”, Preprinty IPM im. M. V. Keldysha, 2018, 069, 32 pp.      
24. Yu. A. Alkhutov, O. V. Krasheninnikova, “Remark on the Hӧlder Continuity of p(x)-Harmonic Functions”, J Math Sci, 216:2 (2016), 147