Hölder regularity and Harnack inequality for degenerate parabolic equations related to Caffarelli–Kohn–Nirenberg inequalities

2004 ◽  
Vol 57 (7-8) ◽  
pp. 971-1003 ◽  
Author(s):  
B. Abdellaoui ◽  
I.Peral Alonso
Keyword(s):  
Harnack Inequality ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Degenerate Parabolic ◽  
Holder Regularity

scholarly journals Hölder regularity for degenerate parabolic equations with variable exponents

2022 ◽  
Vol 40 ◽  
pp. 1-19
Author(s):  
Hamid EL Bahja
Keyword(s):  
Weak Solutions ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equations ◽  
Hölder Regularity ◽  
Variable Exponents ◽  
Young’S Inequality ◽  
Scaling Method ◽  
Degenerate Parabolic ◽  
Young's Inequality ◽  
Holder Regularity

In this paper, we discuss a class of degenerate parabolic equations with variable exponents. By  using the Steklov average and Young's inequality, we establish energy and logarithmicestimates for solutions to these equations. Then based on the intrinsic scaling method, we provethat local weak solutions are locally continuous.

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