Strong solutions of evolution equations with p(x,t)-Laplacian: Existence, global higher integrability of the gradients and second-order regularity
نویسندگان
چکیده
We study the homogeneous Dirichlet problem for degenerate parabolic equationut?div(|?u|p(x,t)?2?u)=f(x,t) in QT=?×(0,T), where ??RN, N?2, is a bounded domain with boundary ???C2. The variable exponent p(x,t) given Lipschitz-continuous function, p(x,t):QT?[p?,p+] some constants 2NN+265, then Dxj(|?u|p(x,t)?22Dxiu)?L2(QT). Moreover, possesses property higher integrability gradient:|?u|p(x,t)+??L1(QT)for every 02 part QT. same results are proved equation regularized fluxes (?2+|?u|2)p(x,t)?22?u, ?>0.
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2021
ISSN: ['0022-247X', '1096-0813']
DOI: https://doi.org/10.1016/j.jmaa.2020.124506