Moser-Trudinger inequality involving the anisotropic Dirichlet norm \((\int_\Omega F^N(\nabla u) d x)^{\frac{1}{N}}\) on \(W_0^{1, N}(\Omega)\)

DOI10.1016/j.jfa.2018.12.001zbMath1409.35014OpenAlexW2904404572MaRDI QIDQ1731879

Changliang Zhou, Chunqin Zhou

Publication date: 14 March 2019

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2018.12.001

zbMATH Keywords

blow-up analysisFinsler Laplacianexistence of extremal functionsLions type concentration-compactness

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Quasilinear elliptic equations (35J62) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

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Cites Work

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• An improved Hardy-Trudinger-Moser inequality
• A priori estimates and blow-up behavior for solutions of \(-Q_Nu = Ve^u\) in bounded domain in \(\mathbb R^N\)
• A Hardy-Moser-Trudinger inequality
• Blow-up analysis concerning singular Trudinger-Moser inequalities in dimension two
• Blow-up analysis of a Finsler-Liouville equation in two dimensions
• A characterization of the Wulff shape by an overdetermined anisotropic PDE
• Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions
• A sharp form of Moser-Trudinger inequality in high dimension
• Sharp constant and extremal function for the improved Moser-Trudinger inequality involving \(L^p\) norm in two dimension
• Critical points of embeddings of \(H_ 0^{1,n}\) into Orlicz spaces
• Regularity for a more general class of quasilinear equations
• Extremal functions for the Trudinger-Moser inequality in 2 dimensions
• Anisotropic motion by mean curvature in the context of Finsler geometry
• Convex symmetrization and applications
• Isoperimetric inequalities, Wulff shape and related questions for strongly nonlinear elliptic operators
• Positive solutions of critical semilinear elliptic equations on non-contractible planar domains
• Extremal functions of Moser-Trudinger inequality involving Finsler-Laplacian
• Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs
• When does a perturbed Moser-Trudinger inequality admit an extremal?
• Extremal functions for Trudinger-Moser inequalities of Adimurthi-Druet type in dimension two
• Extremal functions for singular Moser-Trudinger embeddings
• The Moser-Trudinger inequality and its extremals on a disk via energy estimates
• Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
• Improved Moser-Trudinger Inequality Involving L^p Norm in n Dimensions
• Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
• Remarks on a Finsler-Laplacian
• Boundary regularity for solutions of degenerate elliptic equations
• A uniqueness proof for the Wulff Theorem
• Uniform estimates and blow–up behavior for solutions of −δ(u)=v(x)e^uin two dimensions
• Extremal functions for Moser’s inequality