A proof of Hessian Sobolev inequality

DOI10.1016/j.na.2011.03.017zbMath1217.35066OpenAlexW1999631986MaRDI QIDQ540258

Shuxuan Li

Publication date: 1 June 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.2011.03.017

zbMATH Keywords

a priori estimatesHessian Sobolev inequalityHessian equation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45)

Related Items

The Sobolev inequality for complex Hessian equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Remarks on critical exponents for Hessian operators
• Moser-Trudinger type inequalities for the Hessian equation
• The Dirichlet problem for nonlinear second order elliptic equations. III: Functions of the eigenvalues of the Hessian
• A Poincaré type inequality for Hessian integrals
• Hessian measures. II
• The Yamabe problem for higher order curvatures
• On a fully nonlinear Yamabe problem
• The k-Hessian Equation
• A variational theory of the Hessian equation