A note on minimizing the Moser--Trudinger functional of high order derivatives

DOI10.1016/j.na.2007.06.043zbMath1162.46021OpenAlexW2013147284MaRDI QIDQ943694

Qingyue Liu, Yun Yan Yang

Publication date: 10 September 2008

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.2007.06.043

zbMATH Keywords

Moser-Trudinger inequalityblowing up analysis

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Boundary value problems for higher-order elliptic equations (35J40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Existence theories for free problems in two or more independent variables (49J10) Existence theories for optimal control problems involving partial differential equations (49J20) Variational methods for higher-order elliptic equations (35J35)

Cites Work

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• A sharp inequality of J. Moser for higher order derivatives
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• Classification of solutions of higher order conformally invariant equations
• Sharp borderline Sobolev inequalities on compact Riemannian manifolds
• A classification of solutions of a conformally invariant fourth order equation in \(\mathbb{R}^n\)
• Elliptic partial differential equations of second order
• A Moser-Trudinger inequality on the boundary of a compact Riemann surface
• Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds
• Blow-up Analysis in Dimension 2 and a Sharp Form of Trudinger–Moser Inequality
• Locating the peaks of solutions via the maximum principle II: A local version of the method of moving planes
• Extremal functions for Moser’s inequality
• EXTREMAL FUNCTIONS FOR MOSER–TRUDINGER INEQUALITIES ON 2-DIMENSIONAL COMPACT RIEMANNIAN MANIFOLDS WITH BOUNDARY

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