On positive supersolutions of fractional elliptic equations with gradient terms

DOI10.1007/s41980-023-00814-3zbMath1527.35478OpenAlexW4386799845MaRDI QIDQ6071323

Nguyen Thi Thuy Quynh

Publication date: 23 November 2023

Published in: Bulletin of the Iranian Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s41980-023-00814-3

zbMATH Keywords

fractional Laplaciangradient termsLiouville-type theorempositive supersolutions

Mathematics Subject Classification ID

Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Fractional partial differential equations (35R11) Liouville theorems and Phragmén-Lindelöf theorems in context of PDEs (35B53)

Cites Work

• Unnamed Item
• Unnamed Item
• Regularity for the supercritical fractional Laplacian with drift
• Radial fractional Laplace operators and Hessian inequalities
• Optimal regularity of solutions to the obstacle problem for the fractional Laplacian with drift
• Perturbations of Lane-Emden and Hamilton-Jacobi equations: the full space case
• Liouville theorems for supersolutions of semilinear elliptic equations with drift terms in exterior domains
• Regularity of the free boundary for the obstacle problem for the fractional Laplacian with drift
• Global well-posedness for an advection-diffusion equation arising in magneto-geostrophic dynamics
• Fundamental solutions and Liouville type theorems for nonlinear integral operators
• On divergence-free drifts
• Dirichlet heat kernel estimates for fractional Laplacian with gradient perturbation
• The explosion problem in a flow
• Liouville-type results for semilinear elliptic equations in unbounded domains
• The proof of the Lane-Emden conjecture in four space dimensions
• The obstacle problem for the fractional Laplacian with critical drift
• A priori bounds and positive solutions for non-variational fractional elliptic systems.
• Liouville type theorems for stable solutions of the weighted elliptic system with the advection term: \(p \geq \vartheta >1\)
• Remark on some conformally invariant integral equations: the method of moving spheres
• The speed of propagation for KPP type problems. I: Periodic framework
• A priori estimates and existence of positive solutions of nonlinear cooperative elliptic systems
• Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
• Liouville type theorems for elliptic equations with gradient terms
• Liouville type theorems for nonlinear elliptic equations and systems involving fractional Laplacian in the half space
• Study of the existence of supersolutions for nonlocal equations with gradient terms
• Liouville type theorems for fractional and higher-order fractional systems
• A note on positive supersolutions of the fractional Lane-Emden system
• On the classification of positive supersolutions of elliptic systems involving the advection terms
• Liouville theorems for fractional Hénon equation and system on \(\mathbb{R}^n\)
• Stability of entire solutions to supercritical elliptic problems involving advection
• A Liouville type theorem for an integral system
• Symmetry of components and Liouville-type theorems for semilinear elliptic systems involving the fractional Laplacian
• A note on the nonexistence of positive supersolutions to elliptic equations with gradient terms
• On some nonlocal elliptic systems with gradient source terms
• Liouville's theorem for the drifting Laplacian
• On stable entire solutions of semi-linear elliptic equations with weights
• Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Global and local behavior of positive solutions of nonlinear elliptic equations
• A rellich type identity and applications
• Existence results of positive solutions for nonlinear cooperative elliptic systems involving fractional Laplacian
• Heat kernel estimates for Dirichlet fractional Laplacian with gradient perturbation
• A Liouville type theorem for non-linear elliptic systems involving advection terms
• Uniqueness and monotonicity of solutions for fractional equations with a gradient term
• Optimal Liouville-type theorems for a system of parabolic inequalities
• Classification of solutions for an integral equation
• Liouville type results for systems of equations involving fractional Laplacian in exterior domains

This page was built for publication: On positive supersolutions of fractional elliptic equations with gradient terms