Аннотация:
В работе доказана непрерывность по Гёльдеру решений параболического уравнения, содержащего p(x,t)p(x,t)-лапласиан. На показатель pp накладывается так называемое логарифмическое условие.
Образец цитирования:
Ю. А. Алхутов, В. В. Жиков, “Гёльдеровская непрерывность решений параболических уравнений с переменным порядком нелинейности”, Тр. сем. им. И. Г. Петровского, 28, Изд-во Моск. ун-та, М., 2011, 8–74; J. Math. Sci. (N. Y.), 179:3 (2011), 347–389
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
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
М. Д. Сурначёв, “Неравенство Харнака слабого типа
для параболического p(x)p(x)-лапласиана”, Матем. заметки, 111:1 (2022), 149–153; M. D. Surnachev, “Harnack's Inequality of Weak Type for the Parabolic p(x)p(x)-Laplacian”, Math. Notes, 111:1 (2022), 161–165
Igor I. Skrypnik, Mykhailo V. Voitovych, “On the continuity of solutions of quasilinear parabolic equations with generalized Orlicz growth under non-logarithmic conditions”, Annali di Matematica, 201:3 (2022), 1381
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)
Mikhail Surnachev, “On the weak Harnack inequality for the parabolic p ( x )-Laplacian”, ASY, 130:1-2 (2022), 127
Hamid El Bahja, “Local continuity of singular anisotropic parabolic equations with variable growth”, Complex Variables and Elliptic Equations, 66:12 (2021), 1998
Stanislav Antontsev, Sergey Shmarev, “Global estimates for solutions of singular parabolic and elliptic equations with variable nonlinearity”, Nonlinear Analysis, 195 (2020), 111724
Hamid El Bahja, “Hölder continuity of singular parabolic equations with variable nonlinearity”, Analele Universitatii “Ovidius” Constanta - Seria Matematica, 28:3 (2020), 51
Igor I. Skrypnik, Mykhailo V. Voitovych, “B1 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
Mengyao Ding, Chao Zhang, Shulin Zhou, “Global boundedness and Hölder regularity of solutions to general p(x,t)‐Laplace parabolic equations”, Math Methods in App Sciences, 43:9 (2020), 5809
S. Antontsev, S. Shmarev, “Higher regularity of solutions of singular parabolic equations with variable nonlinearity”, Applicable Analysis, 98:1-2 (2019), 310
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
Stanislav Antontsev, Ivan Kuznetsov, Sergey Shmarev, “Global higher regularity of solutions to singular p(x,t)-parabolic equations”, Journal of Mathematical Analysis and Applications, 466:1 (2018), 238
Jihoon Ok, “Regularity for parabolic equations with time dependent growth”, Journal de Mathématiques Pures et Appliquées, 120 (2018), 253
Sergey Shmarev, “On the continuity of solutions of the nonhomogeneous evolutionp(x,t)-Laplace equation”, Nonlinear Analysis, 167 (2018), 67
Цитирование в формате AMSBIB
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