A note on borderline Brezis-Nirenberg type problems
Julian Haddad, Marcos Montenegro
TL;DR
This paper investigates how ellipticity points on the boundary influence solutions to a class of elliptic boundary value problems similar to the Brezis-Nirenberg problem, highlighting boundary effects on solution existence.
Contribution
It provides new insights into the role of boundary ellipticity points in the Brezis-Nirenberg type problems for divergence form elliptic operators.
Findings
Ellipticity points significantly affect solution behavior.
Boundary geometry influences existence of solutions.
New conditions for solution existence are identified.
Abstract
We study the effect of ellipticity points on the boundary in the Brezis-Nirenberg problem for elliptic operators in divergence form.
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