New types of Caffarelli-Kohn-Nirenberg inequalities and applications

DOI10.3934/cpaa.2022135OpenAlexW4297721103MaRDI QIDQ2099232

Zongming Guo, XiaoHong Guan

Publication date: 23 November 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2022135

zbMATH Keywords

positive solutionsCaffarelli-Kohn-Nirenberg inequalitiesweighted fourth order elliptic equationsembeddings of weighted Sobolev spaces

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Positive solutions to PDEs (35B09) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (1)

Classification and non-degeneracy of positive radial solutions for a weighted fourth-order equation and its application

Cites Work

• Unnamed Item
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• Entire solutions for a class of fourth-order semilinear elliptic equations with weights
• Sobolev type embedding and weak solutions with a prescribed singular set
• Weighted Sobolev spaces of radially symmetric functions
• Bessel pairs and optimal Hardy and Hardy-Rellich inequalities
• Sobolev spaces of symmetric functions and applications
• On Caffarelli-Kohn-Nirenberg-type inequalities for the weighted biharmonic operator in cones
• Existence and stability of entire solutions to a semilinear fourth order elliptic problem
• The critical dimension for a fourth-order elliptic problem with singular nonlinearity
• Classification of solutions of higher order conformally invariant equations
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Non-existence results for semilinear cooperative elliptic systems via moving spheres
• Radial symmetry of entire solutions of a bi-harmonic equation with exponential nonlinearity
• Bôcher-type results for the fourth and higher order equations on singular manifolds with conical metrics
• Singularity and decay estimates in superlinear problems via Liouville-type theorems. I: Elliptic equations and systems
• The Gel'fand problem for the biharmonic operator
• Further study of entire radial solutions of a biharmonic equation with exponential nonlinearity
• Radial entire solutions for supercritical biharmonic equations
• Critical exponents, critical dimensions and the biharmonic operator
• Qualitative properties of entire radial solutions for a biharmonic equation with supercritical nonlinearity
• Optimal weighted Hardy-Rellich inequalities on H ² ∩ H ₀ ¹
• On a Fourth Order Nonlinear Elliptic Equation with Negative Exponent
• Harnack's inequality for cooperative weakly coupled elliptic systems
• Functional Inequalities: New Perspectives and New Applications
• Embeddings of weighted Sobolev spaces and a weighted fourth-order elliptic equation
• A Semilinear Fourth Order Elliptic Problem with Exponential Nonlinearity
• Stable Solutions for the Bilaplacian with Exponential Nonlinearity
• Asymptotic behavior at the isolated singularities of solutions of some equations on singular manifolds with conical metrics

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