Gradient estimates for divergence form parabolic systems from composite materials

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Hongjie Dong ◽  
Longjuan Xu
Keyword(s):  
Composite Materials ◽  
Parabolic Systems ◽  
Divergence Form ◽  
Gradient Estimates

Parabolic systems with measurable coefficients in weighted Orlicz spaces

2016 ◽  
Vol 18 (02) ◽  
pp. 1550018 ◽  
Author(s):  
Sun-Sig Byun ◽  
Jihoon Ok ◽  
Dian K. Palagachev ◽  
Lubomira G. Softova
Keyword(s):  
Weak Solution ◽  
Orlicz Space ◽  
Parabolic System ◽  
Time Domain ◽  
Orlicz Spaces ◽  
Parabolic Systems ◽  
Divergence Form ◽  
Space Time ◽  
Spatial Gradient ◽  
Measurable Coefficients

We consider a parabolic system in divergence form with measurable coefficients in a cylindrical space–time domain with nonsmooth base. The associated nonhomogeneous term is assumed to belong to a suitable weighted Orlicz space. Under possibly optimal assumptions on the coefficients and minimal geometric requirements on the boundary of the underlying domain, we generalize the Calderón–Zygmund theorem for such systems by essentially proving that the spatial gradient of the weak solution gains the same weighted Orlicz integrability as the nonhomogeneous term.

scholarly journals Gradient Estimates for Divergence Form Elliptic Systems Arising from Composite Material

2019 ◽  
Vol 51 (3) ◽  
pp. 2444-2478 ◽  
Author(s):  
Hongjie Dong ◽  
Longjuan Xu
Keyword(s):  
Composite Material ◽  
Elliptic Systems ◽  
Divergence Form ◽  
Gradient Estimates

Gradient estimates for a class of parabolic systems

2007 ◽  
Vol 136 (2) ◽  
pp. 285-320 ◽  
Author(s):  
Emilio Acerbi ◽  
Giuseppe Mingione
Keyword(s):  
Parabolic Systems ◽  
Gradient Estimates

Quasi-linear parabolic systems in divergence form with weak monotonicity

2001 ◽  
Vol 107 (3) ◽  
pp. 497-520 ◽  
Author(s):  
Norbert Hungerbühler
Keyword(s):  
Parabolic Systems ◽  
Divergence Form ◽  
Weak Monotonicity
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