fast diffusion equations
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2019 ◽  
Vol 9 (1) ◽  
pp. 327-360 ◽  
Author(s):  
Rakesh Arora ◽  
Jacques Giacomoni ◽  
Guillaume Warnault

Abstract In this work, we establish a new Picone identity for anisotropic quasilinear operators, such as the p(x)-Laplacian defined as div(|∇ u|p(x)−2 ∇ u). Our extension provides a new version of the Diaz-Saa inequality and new uniqueness results to some quasilinear elliptic equations with variable exponents. This new Picone identity can be also used to prove some accretivity property to a class of fast diffusion equations involving variable exponents. Using this, we prove for this class of parabolic equations a new weak comparison principle.


2017 ◽  
Vol 10 (1) ◽  
pp. 33-59 ◽  
Author(s):  
Matteo Bonforte ◽  
◽  
Jean Dolbeault ◽  
Matteo Muratori ◽  
Bruno Nazaret ◽  
...  

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