Sharp Trudinger-Moser inequalities with homogeneous weights

Abstract

We investigate sharp Trudinger-Moser type inequalities with the homogeneous weight satisfying a natural curvature-dimension bound condition. Also we study the optimal versions of these inequalities with best constants on both finite and infinite volume domains on Euclidean spaces.

Keywords

• Trudinger-Moser inequalities
• homogeneous weights
• best constants
• critical growth
• exact growth condition