The Brezis-Nirenberg problem for fractional elliptic operators
Ko-Shin Chen, Marcos Montenegro, Xiaodong Yan
TL;DR
This paper investigates how fractional elliptic operators influence the existence of positive solutions in a nonlocal Brezis-Nirenberg problem, expanding understanding of boundary value problems involving fractional operators.
Contribution
It introduces new results on the existence and nonexistence of solutions for fractional elliptic operators in bounded domains, extending classical Brezis-Nirenberg theory.
Findings
Conditions for existence of positive solutions
Conditions for nonexistence of solutions
Impact of fractional order on solution behavior
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.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Advanced Mathematical Modeling in Engineering · Numerical methods in inverse problems