L∞ – Estimate for Qualitatively Bounded Weak Solutions of Nonlinear Degenerate Diagonal Parabolic Systems

1996 ◽  
Vol 2 (1) ◽  
pp. 1-12
Author(s):  
W. M. Zaja̧czkowski
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Nonlinear Degenerate ◽  
Bounded Weak Solutions

scholarly journals Lp Estimates for Weak Solutions to Nonlinear Degenerate Parabolic Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Na Wei ◽  
Xiangyu Ge ◽  
Yonghong Wu ◽  
Leina Zhao
Keyword(s):  
Weak Solutions ◽  
Vector Fields ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Lp Estimates ◽  
Reverse Hölder Inequalities ◽  
Degenerate Parabolic Systems ◽  
Degenerate Parabolic ◽  
Reverse Hölder ◽  
Nonlinear Degenerate

This paper is devoted to the Lp estimates for weak solutions to nonlinear degenerate parabolic systems related to Hörmander’s vector fields. The reverse Hölder inequalities for degenerate parabolic system under the controllable growth conditions and natural growth conditions are established, respectively, and an important multiplicative inequality is proved; finally, we obtain the Lp estimates for the weak solutions by combining the results of Gianazza and the Caccioppoli inequality.

scholarly journals Very weak solutions of parabolic systems of p-Laplacian type

2002 ◽  
Vol 40 (1) ◽  
pp. 105-132 ◽  
Author(s):  
Juha Kinnunen ◽  
John L. Lewis
Keyword(s):  
Weak Solutions ◽  
Parabolic Systems ◽  
Very Weak Solutions

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.

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