scholarly journals Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule

2005 ◽  
Vol 307 (2) ◽  
pp. 736-752 ◽  
Author(s):  
Yousong Luo ◽  
Andrew Eberhard
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Sum Rule ◽  
Comparison Principles

On the viscosity solutions of eigenvalue problems for a class of nonlinear elliptic equations

2019 ◽  
Vol 12 (4) ◽  
pp. 393-421
Author(s):  
Tilak Bhattacharya ◽  
Leonardo Marazzi
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Eigenvalue Problems ◽  
A Priori ◽  
Nonlinear Elliptic Equations ◽  
First Eigenvalue ◽  
Nonlinear Elliptic ◽  
Degenerate Elliptic ◽  
First Eigenfunction ◽  
Nonlinear Degenerate

AbstractWe consider viscosity solutions of a class of nonlinear degenerate elliptic equations, involving a parameter, on bounded domains. These arise in the study of eigenvalue problems. We prove comparison principles and a priori supremum bounds for the solutions. We also address the eigenvalue problem and, in many instances, show the existence of the first eigenvalue and an associated positive first eigenfunction.

scholarly journals Coupling Lévy measures and comparison principles for viscosity solutions

2019 ◽  
Vol 372 (10) ◽  
pp. 7327-7370
Author(s):  
Nestor Guillen ◽  
Chenchen Mou ◽  
Andrzej Świȩch
Keyword(s):  
Viscosity Solutions ◽  
Comparison Principles ◽  
Lévy Measures
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