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Principal eigenvalues and eigenfunctions for fully nonlinear equations in punctured balls.
- Source :
-
Journal de Mathematiques Pures et Appliquees . Jun2024, Vol. 186, p74-102. 29p. - Publication Year :
- 2024
-
Abstract
- This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we analyze existence, uniqueness and regularity of solutions ( λ ¯ γ , u γ) of the equation F (D 2 u γ) + λ ¯ γ u γ r γ = 0 in B (0 , 1) ∖ { 0 } , u γ = 0 on ∂ B (0 , 1) where u γ > 0 in B (0 , 1) ∖ { 0 } and γ > 0. We prove existence of radial solutions which are continuous on B (0 , 1) ‾ in the case γ < 2 , existence of unbounded solutions in the case γ = 2 and a non existence result for γ > 2. We also give, in the case of Pucci's operators, the explicit value of λ ¯ 2 , which generalizes the Hardy–Sobolev constant for the Laplacian. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00217824
- Volume :
- 186
- Database :
- Academic Search Index
- Journal :
- Journal de Mathematiques Pures et Appliquees
- Publication Type :
- Academic Journal
- Accession number :
- 177653213
- Full Text :
- https://doi.org/10.1016/j.matpur.2024.04.004