Mathematics – Analysis of PDEs
Scientific paper
2009-09-03
Mathematics
Analysis of PDEs
This version gives the credit to an independently proved result, missed in the early version, and corrects an error in one of
Scientific paper
The paper raises a question about the optimal critical nonlinearity for the Sobolev space in two dimensions, connected to loss of compactness, and discusses the pertinent concentration compactness framework. We study properties of the improved version of the Trudinger-Moser inequality on the open unit disk $B\subset\R^2$, recently proved by G. Mancini and K. Sandeep. Unlike the original Trudinger-Moser inequality, this inequality is invariant with respect to M\"obius automorphisms of the unit disk, and as such is a closer analogy of the critical nonlinearity $\int |u|^{2^*}$ in the higher dimension than the original Trudinger-Moser nonlinearity.
Adimurthi
Tintarev Kyril
No associations
LandOfFree
On a version of Trudinger-Moser inequality with Möbius shift invariance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with On a version of Trudinger-Moser inequality with Möbius shift invariance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a version of Trudinger-Moser inequality with Möbius shift invariance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-664098