Liouville theorem for poly-harmonic functions on \(\mathbb{R}^n_+ \)

DOI10.1007/S00013-020-01464-1zbMath1445.35096OpenAlexW3017073938MaRDI QIDQ2193027

Guolin Qin, Wei Dai

Publication date: 24 August 2020

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-020-01464-1

zbMATH Keywords

super poly-harmonic propertiesharmonic asymptotic expansionsNavier problems

Mathematics Subject Classification ID

Higher-order elliptic equations (35J30) Semilinear elliptic equations with Laplacian, bi-Laplacian or poly-Laplacian (35J91) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Related Items (3)

On properties of positive solutions to nonlinear tri-harmonic and bi-harmonic equations with negative exponents ⋮ Maximum principles and the method of moving planes for the uniformly elliptic nonlocal Bellman operator and applications ⋮ Super poly-harmonic properties, Liouville theorems and classification of nonnegative solutions to equations involving higher-order fractional Laplacians

Cites Work

• Unnamed Item
• Unnamed Item
• A Liouville theorem for \(\alpha\)-harmonic functions in \(\mathbb{R}^n_+\)
• Classification theorems for solutions of higher order boundary conformally invariant problems. I.
• Liouville type theorems for PDE and IE systems involving fractional Laplacian on a half space
• Integral representations of harmonic functions in half spaces
• Classification of solutions of higher order conformally invariant equations
• On uniqueness of solutions of \(n\)-th order differential equations in conformal geometry
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Classification of nonnegative classical solutions to third-order equations
• Uniqueness theorems through the method of moving spheres
• Liouville theorems involving the fractional Laplacian on a half space
• Liouville type theorem for higher order Hénon equations on a half space
• Super poly-harmonic property of solutions for Navier boundary problems on a half space
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Classification of nonnegative solutions to a bi-harmonic equation with Hartree type nonlinearity
• Notions of convexity

This page was built for publication: Liouville theorem for poly-harmonic functions on \(\mathbb{R}^n_+ \)