Positive Solutions of Quasilinear Elliptic Equations with Fuchsian Potentials in Wolff Class

Using Harnack’s inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂ Ω ∪ { ∞ } for the quasilinear elliptic equation - div ( | ∇ u | A p - 2 A ∇ u ) + V | u | p - 2 u = 0 in Ω , where Ω is a domain...

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Bibliographic Details
Published in:Milan journal of mathematics 2023-06, Vol.91 (1), p.59-96
Main Authors: Giri, Ratan Kr, Pinchover, Yehuda
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary:Using Harnack’s inequality and a scaling argument we study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂ Ω ∪ { ∞ } for the quasilinear elliptic equation - div ( | ∇ u | A p - 2 A ∇ u ) + V | u | p - 2 u = 0 in Ω , where Ω is a domain in R d , d ≥ 2 , 1 < p < d , and A = ( a ij ) ∈ L loc ∞ ( Ω ; R d × d ) is a symmetric and locally uniformly positive definite matrix. It is assumed that the potential V belongs to a certain Wolff class and has a generalized Fuchsian-type singularity at an isolated point ζ ∈ ∂ Ω ∪ { ∞ } .
ISSN:1424-9286
1424-9294
DOI:10.1007/s00032-023-00377-2