A Brezis-Nirenberg problem on hyperbolic spaces
Carriao, Paulo Cesar
Miyagaki, Oliimpio Hiroshi
Texas State University, Department of Mathematics
We consider a Brezis-Nirenberg problem on the hyperbolic space ℍn. By using the stereographic projection, the problem becomes a singular problem on the boundary of the open ball B1(0) ⊂ ℝn. Thanks to the Hardy inequality, in a version due to Brezis-Marcus, the difficulty involving singularities can be overcame. We use the mountain pass theorem due to Ambrosetti-Rabinowitz and Brezis-Nirenberg arguments to obtain a nontrivial solution.
Variational method, Critical point, Critical exponent, Hyperbolic manifold
Carrião, P. C., Lehrer, R., Miyagaki, O. H., & Vicente, A. (2019). A Brezis-Nirenberg problem on hyperbolic spaces. <i>Electronic Journal of Differential Equations, 2019</i>(67), pp. 1-15.