The Brezis-Nirenberg problem for fractional elliptic operators

2016/01/08 by Chen, Ko-Shin, Montenegro, Marcos, Yan, Xiaodong
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1601.01766

Abstract

In the present paper, we study the effect of an elliptic operator in divergence form L defined in a bounded open set on the existence and nonexistence of positive solutions of the associated nonlocal Brezis-Nirenberg problem involving powers of L.

Related

• The Brezis-Nirenberg problem for nonlocal systems
• A Brezis-Nirenberg type result for mixed local and nonlocal operators
• The Brezis-Nirenberg problem for the fractional p-Laplacian
• Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings
• On the existence of multiple solutions for fractional Brezis Nirenberg type equations