scholarly journals Local L∞-estimates, weak Harnack inequality, and stochastic continuity of solutions of SPDEs

2017 ◽  
Vol 262 (1) ◽  
pp. 615-632 ◽  
Author(s):  
Konstantinos Dareiotis ◽  
Máté Gerencsér
Keyword(s):  
Harnack Inequality ◽  
Continuity Of Solutions ◽  
Stochastic Continuity ◽  
Weak Harnack Inequality

On the continuity of solutions of the equations of a porous medium and the fast diffusion with weighted and singular lower-order terms

2021 ◽  
Vol 18 (1) ◽  
pp. 104-139
Author(s):  
Yevhen Zozulia
Keyword(s):  
Porous Medium ◽  
Parabolic Equation ◽  
Harnack Inequality ◽  
Lower Order ◽  
Riesz Potential ◽  
Fast Diffusion ◽  
Right Hand ◽  
Continuity Of Solutions ◽  
The Right ◽  
Lower Order Terms

For the parabolic equation $$ \ v\left(x \right)u_{t} -{div({\omega(x)u^{m-1}}} \nabla u) = f(x,t)\: ,\; u\geq{0}\:,\; m\neq{1} $$ we prove the continuity and the Harnack inequality for generalized k solutions, by using the weighted Riesz potential on the right-hand side of the equation.

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
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