monotonicity formula
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2021 ◽  
Vol 2012 (1) ◽  
pp. 012077
Author(s):  
Ruizhe Wan
Keyword(s):  




2020 ◽  
Vol 2020 (758) ◽  
pp. 95-137 ◽  
Author(s):  
Nick Edelen

AbstractWe develop the notion of Brakke flow with free-boundary in a barrier surface. Unlike the classical free-boundary mean curvature flow, the free-boundary Brakke flow must “pop” upon tangential contact with the barrier. We prove a compactness theorem for free-boundary Brakke flows, define a Gaussian monotonicity formula valid at all points, and use this to adapt the local regularity theorem of White [23] to the free-boundary setting. Using Ilmanen’s elliptic regularization procedure [10], we prove existence of free-boundary Brakke flows.



2020 ◽  
Vol 2 (4) ◽  
pp. 657-679
Author(s):  
Fausto Ferrari ◽  
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Nicolò Forcillo ◽  
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...  
Keyword(s):  




2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Abdellaziz Harrabi ◽  
Cherif Zaidi

Abstract In this paper, we are concerned with Liouville-type theorems of the Hénon Lane–Emden triharmonic equations in whole space. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the Pohozaev-type identity, monotonicity formula of solutions and a blowing down sequence.



2018 ◽  
Vol 97 (1) ◽  
pp. 49-51
Author(s):  
D. E. Apushkinskaya ◽  
N. N. Uraltseva
Keyword(s):  




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