Issue |
ESAIM: COCV
Volume 27, 2021
|
|
---|---|---|
Article Number | 39 | |
Number of page(s) | 17 | |
DOI | https://doi.org/10.1051/cocv/2021037 | |
Published online | 30 April 2021 |
A singular elliptic equation and a related functional*
1
Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli” Viale Lincoln 5,
81100
Caserta, Italy.
2
Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli Federico II, Complesso Monte S. Angelo, Via Cintia,
80126
Napoli, Italy.
3
Departament d’Anàlisi Matemàtica, Universitat de València,
Dr. Moliner 50,
46100
Burjassot,
València, Spain.
** Corresponding author: mercaldo@unina.it
Received:
26
July
2019
Accepted:
1
April
2021
We study a class of Dirichlet boundary value problems whose prototype is
where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|p−2u and a datum f which possibly changes its sign. We introduce a notion of solution in this singular setting and we prove an existence result for such a solution. The motivation of our notion of solution to problem above is due to a minimization problem for a non–differentiable functional on whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
Mathematics Subject Classification: 35B25 / 35B27 / 35J25 / 35J67
Key words: Semilinear equations / singularity at u = 0 / existence / uniqueness
© EDP Sciences, SMAI 2021
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.