Quasilinear Elliptic Equations Involving Variable Exponents

2008 ◽  
Author(s):  
Mihai Mihăilescu ◽  
Gheorghe Moroşanu
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Variable Exponents ◽  
Quasilinear Elliptic

scholarly journals A Picone identity for variable exponent operators and applications

2019 ◽  
Vol 9 (1) ◽  
pp. 327-360 ◽  
Author(s):  
Rakesh Arora ◽  
Jacques Giacomoni ◽  
Guillaume Warnault
Keyword(s):  
Parabolic Equations ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Fast Diffusion ◽  
Variable Exponents ◽  
Uniqueness Results ◽  
Picone Identity ◽  
Weak Comparison Principle ◽  
Quasilinear Elliptic ◽  
Fast Diffusion Equations

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.

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