On the weak Harnack inequality for the parabolic p ( x )-Laplacian

2021 ◽  
pp. 1-39
Author(s):  
Mikhail Surnachev
Keyword(s):  
Harnack Inequality ◽  
Weak Harnack Inequality

In this paper a weak Harnack inequality for the parabolic p ( x )-Laplacian is established.

scholarly journals The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth

2021 ◽  
Vol 275 ◽  
pp. 790-814
Author(s):  
Allami Benyaiche ◽  
Petteri Harjulehto ◽  
Peter Hästö ◽  
Arttu Karppinen
Keyword(s):  
Harnack Inequality ◽  
Weak Harnack Inequality

A control condition for a weak Harnack inequality

2012 ◽  
Vol 75 (11) ◽  
pp. 4198-4204 ◽  
Author(s):  
Alessia E. Kogoj
Keyword(s):  
Harnack Inequality ◽  
Weak Harnack Inequality

scholarly journals Remarks on parabolic De Giorgi classes

2021 ◽  
Author(s):  
Naian Liao
Keyword(s):  
Harnack Inequality ◽  
Hölder Continuity ◽  
Holder Continuity ◽  
Type Estimate ◽  
Local Boundedness ◽  
Heavy Machinery ◽  
Weak Harnack Inequality ◽  
Logarithmic Type ◽  
Local Hölder Continuity

AbstractWe make several remarks concerning properties of functions in parabolic De Giorgi classes of order p. There are new perspectives including a novel mechanism of propagating positivity in measure, the reservation of membership under convex composition, and a logarithmic type estimate. Based on them, we are able to give new proofs of known properties. In particular, we prove local boundedness and local Hölder continuity of these functions via Moser’s ideas, thus avoiding De Giorgi’s heavy machinery. We also seize this opportunity to give a transparent proof of a weak Harnack inequality for nonnegative members of some super-class of De Giorgi, without any covering argument.

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