We introduce new sets of functions different both from the space introduced in [Ph. Bénilan, L. Boccardo, T. Gallouёt, R. Gariepy, M. Pierre, and J. L. Vazquez, Ann. Scuola Norm. Super. Pisa, 22, No. 2, 241–273 (1995)] and from the Rakotoson T -set introduced in [J. M. Rakotoson, Different. Integr. Equat., 6, No. 1, 27–36 (1993); J. Different. Equat., 111, No. 2, 458–471 (1994)]. In the new framework of sets, we present some summability results for the entropy solutions of nonlinear parabolic equations.
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 8, pp. 1107–1121, August, 2015.
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Li, F. Certain Regularity of the Entropy Solutions for Nonlinear Parabolic Equations with Irregular Data. Ukr Math J 67, 1247–1263 (2016). https://doi.org/10.1007/s11253-016-1149-x
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DOI: https://doi.org/10.1007/s11253-016-1149-x