Positive Liouville theorem and asymptotic behaviour for (p, A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space

Ratan Kr Giri; Yehuda Pinchover

doi:10.1007/978-3-031-25424-6_5

Positive Liouville theorem and asymptotic behaviour for (p, A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space

Ratan Kr Giri, Yehuda Pinchover

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂Ω∪{∞}of the quasilinear elliptic equation -div(|∇u|_A^p^-²A∇u)+V|u|^p^-²u =0 inΩ\{ζ}, where Ω isadomaininR^d (d ≥ 2), and A = (aij) ∈ L^∞_loc(Ω;R^d^×^d) is a symmetric and locally uniformly positive definite matrix. The potential V lies in a certain local Morrey space (depending on p) and has a Fuchsian-type isolated singularity at ζ .

Original language	English
Title of host publication	Harmonic Analysis and Partial Differential Equations
Subtitle of host publication	In Honor of Vladimir Maz'ya
Pages	107-140
Number of pages	34
ISBN (Electronic)	9783031254246
DOIs	https://doi.org/10.1007/978-3-031-25424-6_5
State	Published - 1 Jan 2023

Keywords

A)-Laplacian
Fuchsian singularity
Liouville theorem (p
Morrey spaces

ASJC Scopus subject areas

General Mathematics
General Physics and Astronomy

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10.1007/978-3-031-25424-6_5

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abstract = "We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂Ω∪{∞}of the quasilinear elliptic equation -div(|∇u|Ap-2A∇u)+V|u|p-2u =0 inΩ\{ζ}, where Ω isadomaininRd (d ≥ 2), and A = (aij) ∈ L∞loc(Ω;Rd×d) is a symmetric and locally uniformly positive definite matrix. The potential V lies in a certain local Morrey space (depending on p) and has a Fuchsian-type isolated singularity at ζ .",

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PY - 2023/1/1

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N2 - We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂Ω∪{∞}of the quasilinear elliptic equation -div(|∇u|Ap-2A∇u)+V|u|p-2u =0 inΩ\{ζ}, where Ω isadomaininRd (d ≥ 2), and A = (aij) ∈ L∞loc(Ω;Rd×d) is a symmetric and locally uniformly positive definite matrix. The potential V lies in a certain local Morrey space (depending on p) and has a Fuchsian-type isolated singularity at ζ .

AB - We study Liouville-type theorems and the asymptotic behaviour of positive solutions near an isolated singular point ζ ∈ ∂Ω∪{∞}of the quasilinear elliptic equation -div(|∇u|Ap-2A∇u)+V|u|p-2u =0 inΩ\{ζ}, where Ω isadomaininRd (d ≥ 2), and A = (aij) ∈ L∞loc(Ω;Rd×d) is a symmetric and locally uniformly positive definite matrix. The potential V lies in a certain local Morrey space (depending on p) and has a Fuchsian-type isolated singularity at ζ .

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KW - Fuchsian singularity

KW - Liouville theorem (p

KW - Morrey spaces

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Positive Liouville theorem and asymptotic behaviour for (p, A)-Laplacian type elliptic equations with Fuchsian potentials in Morrey space

Abstract

Keywords

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