Exponential problem on a compact Riemannian manifold without boundary

DOI10.1016/j.na.2011.08.043zbMath1228.58014OpenAlexW2018899669WikidataQ115343025 ScholiaQ115343025MaRDI QIDQ644212

Liang Zhao

Publication date: 3 November 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.08.043

zbMATH Keywords

exponential growthTrudinger-Moser inequalityAdams-Fontana inequality

Mathematics Subject Classification ID

Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Variational principles in infinite-dimensional spaces (58E30) Elliptic equations on manifolds, general theory (58J05) Variational methods for second-order elliptic equations (35J20)

Related Items (4)

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 ⋮ On a class of nonhomogeneous elliptic equation on compact Riemannian manifold without boundary ⋮ Yamabe type equations on graphs

Cites Work

• A quasi-linear elliptic equation with critical growth on compact Riemannian manifold without boundary
• The concentration-compactness principle in the calculus of variations. The limit case. I
• Adams' inequalities for bi-Laplacian and extremal functions in dimension four
• On a quasilinear nonhomogeneous elliptic equation with critical growth in \(\mathbb R^N\)
• A sharp inequality of J. Moser for higher order derivatives
• On nonhomogeneous elliptic equations involving critical Sobolev exponent
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• Elliptic equations in \(R^ 2\) with nonlinearities in the critical growth range
• Semilinear Dirichlet problems for the \(N\)-Laplacian in \(\mathbb{R}^ N\) with nonlinearities in the critical growth range
• A class of Adams-Fontana type inequalities and related functionals on manifolds
• Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• A sharp form of the Moser-Trudinger inequality on a compact Riemannian surface
• Nontrivial Solution of Semilinear Elliptic Equations with Critical Exponent in R
• EXTREMAL FUNCTIONS FOR MOSER–TRUDINGER INEQUALITIES ON 2-DIMENSIONAL COMPACT RIEMANNIAN MANIFOLDS WITH BOUNDARY
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