Liouville theorems for a family of very degenerate elliptic nonlinear operators

We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators Pk±, defined respectively as the sum of the largest and the smallest k eigenvalues of the Hessian matrix. For the operator Pk+ we obtain r...

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Bibliographic Details
Published in:Nonlinear analysis 2017-09, Vol.161, p.198-211
Main Authors: Birindelli, Isabeau, Galise, Giulio, Leoni, Fabiana
Format: Article
Language:English
Subjects:
Eigenvalues
Fully nonlinear degenerate elliptic equations
Hessian matrices
Laplace transforms
Liouville type results
Nonlinear equations
Operators
Viscosity
Viscosity solutions
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Summary:We prove nonexistence results of Liouville type for nonnegative viscosity solutions of some equations involving the fully nonlinear degenerate elliptic operators Pk±, defined respectively as the sum of the largest and the smallest k eigenvalues of the Hessian matrix. For the operator Pk+ we obtain results analogous to those which hold for the Laplace operator in space dimension k. Whereas, owing to the stronger degeneracy of the operator Pk−, we get totally different results.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2017.06.002