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

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 Quasilinear Degenerated Elliptic Systems with Weighted in Divergence Form with Weak Monotonicity with General Data

2021 ◽  
Vol 12 (06) ◽  
pp. 500-519
Author(s):  
Abdelkrim Barbara ◽  
El Houcine Rami ◽  
Elhoussine Azroul
Keyword(s):  
Elliptic Systems ◽  
Divergence Form ◽  
Weak Monotonicity ◽  
General Data

$L^p-L^q$ ESTIMATES FOR PARABOLIC SYSTEMS IN NON-DIVERGENCE FORM WITH VMO COEFFICIENTS

2006 ◽  
Vol 74 (03) ◽  
pp. 717-736 ◽  
Author(s):  
ROBERT HALLER-DINTELMANN ◽  
HORST HECK ◽  
MATTHIAS HIEBER
Keyword(s):  
Parabolic Systems ◽  
Divergence Form ◽  
Vmo Coefficients
Sign in / Sign up

Export Citation Format

Share Document