scholarly journals Hölder regularity for weak solutions to divergence form degenerate quasilinear parabolic systems

2014 ◽  
Vol 410 (1) ◽  
pp. 375-390 ◽  
Author(s):  
Yan Dong
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Divergence Form ◽  
Hölder Regularity ◽  
Quasilinear Parabolic Systems ◽  
Holder Regularity ◽  
Quasilinear Parabolic

Regularity of weak solutions to linear and quasilinear parabolic systems of non-divergence type with non-smooth in time principal matrix: A(t)-caloric method

2017 ◽  
Vol 29 (5) ◽  
pp. 1039-1064 ◽  
Author(s):  
Arina A. Arkhipova ◽  
Jana Stará
Keyword(s):  
Approximation Method ◽  
Weak Solutions ◽  
Parabolic Systems ◽  
John 1 ◽  
Quasilinear Parabolic Systems ◽  
Regularity Of Weak Solutions ◽  
Divergence Type ◽  
Quasilinear Parabolic

AbstractWe prove a modification of the so-called A(t)-caloric lemma stated in our earlier work with O. John [1] to study regularity of weak solutions to parabolic systems of non-divergence type with non-smooth in time principal matrices. As an application, we prove smoothness results in Morrey and Campanato spaces for linear parabolic systems of non-divergence type by the A(t)-caloric approximation method.

scholarly journals Local Hölder Regularity of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type

CAUCHY ◽  
2021 ◽  
Vol 7 (1) ◽  
pp. 136-141
Author(s):  
Khoirunisa Khoirunisa ◽  
Corina Karim ◽  
M. Muslikh
Keyword(s):  
Weak Solutions ◽  
Poincaré Inequality ◽  
Parabolic Systems ◽  
Hölder Regularity ◽  
Poincare Inequality ◽  
Holder Space ◽  
Hölder Space ◽  
Regularity Of Weak Solutions ◽  
Holder Regularity

In this paper, the Hölder regularity of weak solutions for singular parabolic systems of p-Laplacian type is investigated. By the Poincare inequality, we show that its weak solutions within Hölder space.

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