scholarly journals Maximum principles, Liouville theorem and symmetry results for the fractional g-Laplacian

2021 ◽  
Vol 212 ◽  
pp. 112465
Author(s):  
Sandra Molina ◽  
Ariel Salort ◽  
Hernán Vivas
Keyword(s):  
Liouville Theorem ◽  
Maximum Principles

THE LIOUVILLE THEOREM INVOLVING QUANTUM EFFECT

1986 ◽  
Vol 6 (2) ◽  
pp. 201-211 ◽  
Author(s):  
Keda Bao ◽  
Fusui Liu
Keyword(s):  
Liouville Theorem ◽  
Quantum Effect

scholarly journals Generalized principal eigenvalues of convex nonlinear elliptic operators in ℝN

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anup Biswas ◽  
Prasun Roychowdhury
Keyword(s):  
Eigenvalue Problem ◽  
Principal Eigenvalue ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
Maximum Principles ◽  
Generalized Eigenvalues ◽  
Nonlinear Elliptic ◽  
Generalized Eigenvalue ◽  
General Convex ◽  
Appl Math

AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator which is locally elliptic and positively 1-homogeneous. Generalizing [H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.

A Liouville theorem for the Stokes system in a half-space

2013 ◽  
Vol 195 (1) ◽  
pp. 13-19 ◽  
Author(s):  
H. Jia ◽  
G. Seregin ◽  
V. Sverak
Keyword(s):  
Half Space ◽  
Stokes System ◽  
Liouville Theorem

scholarly journals Gradient estimates for semilinear elliptic systems and other related results

2015 ◽  
Vol 145 (6) ◽  
pp. 1313-1330 ◽  
Author(s):  
Panayotis Smyrnelis
Keyword(s):  
Liouville Theorem ◽  
Elliptic Systems ◽  
Gradient Estimates ◽  
Alternative Form ◽  
Strong Monotonicity ◽  
Energy Tensor ◽  
Planar Domains ◽  
Stress Energy ◽  
General Phase ◽  
Double Well Potential

A periodic connection is constructed for a double well potential defined in the plane. This solution violates Modica's estimate as well as the corresponding Liouville theorem for general phase transition potentials. Gradient estimates are also established for several kinds of elliptic systems. They allow us to prove the Liouville theorem in some particular cases. Finally, we give an alternative form of the stress–energy tensor for solutions defined in planar domains. As an application, we deduce a (strong) monotonicity formula.

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