Symmetry of positive solutions for Lane-Emden systems involving the logarithmic Laplacian
DOI10.1007/s10440-023-00627-wzbMath1530.35356arXiv2210.09110MaRDI QIDQ6183929
Michael Ruzhansky, Vishvesh Kumar, Rong Zhang
Publication date: 4 January 2024
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.09110
fractional Laplacianlogarithmic LaplacianLane-Emden systemsymmetry and monotonicitydirect method of moving planeslogarithmic symbol
Maximum principles in context of PDEs (35B50) Weak solutions to PDEs (35D30) Second-order elliptic systems (35J47) Fractional partial differential equations (35R11) Symmetries, invariants, etc. in context of PDEs (35B06) Comparison principles in context of PDEs (35B51)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlocal diffusion and applications
- Symmetry and non-existence of solutions for a nonlinear system involving the fractional Laplacian
- Qualitative properties of positive solutions to nonlocal critical problems involving the Hardy-Leray potential
- A direct method of moving planes for the fractional Laplacian
- Fundamental solutions and Liouville type theorems for nonlinear integral operators
- The Pohozaev identity for the fractional Laplacian
- An overdetermined problem in Riesz-potential and fractional Laplacian
- Symmetry and related properties via the maximum principle
- Classification of solutions of some nonlinear elliptic equations
- Direct method of moving planes for logarithmic Laplacian system in bounded domains
- On the moving plane method for nonlocal problems in bounded domains
- The Cauchy process and the Steklov problem
- Nonexistence of positive solutions of semilinear elliptic systems in \(\mathbb{R}^ N\)
- Variational methods for non-local operators of elliptic type
- Small order asymptotics for nonlinear fractional problems
- Classification of solutions of an equation related to a conformal log Sobolev inequality
- A direct method of moving planes for the logarithmic Laplacian
- Spectral properties of the logarithmic Laplacian
- A direct method of moving planes for the system of the fractional Laplacian
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Estimates and structure of \(\alpha\)-harmonic functions
- On a fractional Nirenberg problem. I: Blow up analysis and compactness of solutions
- A symmetry problem in potential theory
- Indefinite fractional elliptic problem and Liouville theorems
- Small order asymptotics of the Dirichlet eigenvalue problem for the fractional Laplacian
- A Brascamp-Lieb-Luttinger–type inequality and applications to symmetric stable processes
- Uniqueness of Radial Solutions for the Fractional Laplacian
- A concave—convex elliptic problem involving the fractional Laplacian
- Regularity of the obstacle problem for a fractional power of the laplace operator
- Variational Methods for Nonlocal Fractional Problems
- A rellich type identity and applications
- Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains
- The Dirichlet problem for the logarithmic Laplacian
- An Extension Problem Related to the Fractional Laplacian
- Liouville Type Theorems for Positive Solutions of Elliptic System in ℝN
- Holder estimates for solutions of integro differential equations like the fractional laplace
- Symmetry via antisymmetric maximum principles in nonlocal problems of variable order
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