Concentration-compactness principle associated with Adams' inequality in Lorentz-Sobolev space

Abstract

The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available in non-Euclidean settings. The first proof of the concentration-compactness principle in non-Euclidean setting, such as the Heisenberg group, was given by Li et al. by using a symmetrization-free nonsmooth truncation argument. In this article, we study the concentration-compactness principle of second-order Adams’ inequality in Lorentz-Sobolev space W02L2,q(Ω){W}_{0}^{2}{L}^{2,q}(\Omega ) for all 12q\gt 2.

Keywords

• concentration-compactness principle
• adams’ inequality
• lorentz-sobolev
• 46e30
• 46e35