Gradient estimates for divergence form parabolic systems from composite materials

Autor: Longjuan Xu, Hongjie Dong
Rok vydání: 2021
Předmět:
Zdroj: Calculus of Variations and Partial Differential Equations. 60
ISSN: 1432-0835
0944-2669
DOI: 10.1007/s00526-021-01927-5
Popis: We consider divergence form, second-order strongly parabolic systems in a cylindrical domain with a finite number of subdomains under the assumption that the interfacial boundaries are $$C^{1,\text {Dini}}$$ and $$C^{\gamma _{0}}$$ in the spatial variables and the time variable, respectively. Gradient estimates and piecewise $$C^{1/2,1}$$ -regularity are established when the leading coefficients and data are assumed to be of piecewise Dini mean oscillation or piecewise Holder continuous. Our results improve the previous results in Fan et al. (Electron J Differ Equ 2013:1–24, 2013) and Li and Li (Sci China Math 60(11):2011–2052, 2017) to a large extent, and appear to be the first of its kind for time-dependent subdomains. As a byproduct, we obtain optimal regularity of weak solutions to parabolic transmission problems with $$C^{1,\mu }$$ or $$C^{1,\text {Dini}}$$ interfaces. This gives an extension of a recent result in Caffarelli et al. (Regularity for $$C^{1,\alpha }$$ interface transmission problems. arXiv:2004.07322 [math.AP]) to parabolic systems.
Databáze: OpenAIRE
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