New results concerning Moser-type inequalities in Lorentz-Sobole v spaces

Abstract

We obtain sharp constants concerning the Moser-type inequalities corresponding to the Lorentz-Sobolev space with respect to the norm ||t^1/n-t^1/q|nabla u|^**(t)||_q. We also derive the key estimate for the Concentration-Compactness Principle with respect to the above norm.

Keywords

• Sobolev spaces
• Lorentz-Sobolev spaces
• Moser-Trudinger inequality
• Concentration-Compactness Principle
• Sharp constants