scholarly journals Some Remarks on Singular Solutions of Nonlinear Elliptic Equations III: Viscosity Solutions Including Parabolic Operators

2012 ◽  
Vol 66 (1) ◽  
pp. 109-143 ◽  
Author(s):  
Luis Caffarelli ◽  
Yanyan Li ◽  
Louis Nirenberg
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Singular Solutions ◽  
Nonlinear Elliptic

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.

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