A class of Adams-Fontana type inequalities and related functionals on manifolds

DOI10.1007/s00030-009-0043-8zbMath1189.58007OpenAlexW2040258963MaRDI QIDQ2268887

Yanyan Li

Publication date: 15 March 2010

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-009-0043-8

zbMATH Keywords

Moser-Trudinger inequalitypolyharmonic operatorAdams-Fontana inequality

Mathematics Subject Classification ID

Elliptic equations on manifolds, general theory (58J05) Variational inequalities (global problems) in infinite-dimensional spaces (58E35)

Related Items

A Trudinger-Moser inequality on a compact Riemannian surface involving Gaussian curvature ⋮ A class of semilinear elliptic equations on groups of polynomial growth ⋮ Existence of solutions for a higher order Kirchhoff type problem with exponential critical growth ⋮ Existence of positive solutions to some nonlinear equations on locally finite graphs ⋮ Exponential problem on a compact Riemannian manifold without boundary ⋮ Adams type inequalities and related elliptic partial differential equations in dimension four ⋮ Existence of positive solutions to quasi-linear elliptic equations with exponential growth in the whole Euclidean space ⋮ EXISTENCE OF GLOBAL SOLUTIONS TO SOME NONLINEAR EQUATIONS ON LOCALLY FINITE GRAPHS ⋮ A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary ⋮ Convergence of ground state solutions for nonlinear Schrödinger equations on graphs ⋮ Yamabe type equations on graphs ⋮ Quantization for an elliptic equation with critical exponential growth on compact Riemannian surface without boundary

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Adams' inequalities for bi-Laplacian and extremal functions in dimension four
• A threshold phenomenon for embeddings of \({H^m_0}\) into Orlicz spaces
• A sharp inequality of J. Moser for higher order derivatives
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Existence of solutions for a class of semilinear polyharmonic equations with critical exponential growth
• Elliptic partial differential equations of second order
• Positive solutions in semilinear critical problems for polyharmonic operators
• Quantization for a fourth order equation with critical exponential growth
• Multibumps analysis in dimension 2: quantification of blow-up levels
• A singular Moser-Trudinger embedding and its applications
• On a Class of Nonlinear Second-Order Differential Equations
• A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface
• Asymptotic Profile for a Fourth Order PDE with Critical Exponential Growth in Dimension Four
• On an inequality by N. Trudinger and J. Moser and related elliptic equations
• Brezis-Nirenberg Problem and Coron Problem for Polyharmonic Operators