We study a class of Dirichlet boundary value problems whose prototype is
| $$ |
where 0 < p < 1 and f belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term |u|$$u 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 $$ whose formal Euler–Lagrange equation is an equation of that type. For nonnegative solutions a uniqueness result is obtained.
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Keywords: Semilinear equations, singularity at $$ = 0, existence, uniqueness
@article{COCV_2021__27_1_A41_0,
author = {Ferone, A. and Mercaldo, A. and Segura De Le\'on, S.},
title = {A singular elliptic equation and a related functional},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2021},
publisher = {EDP-Sciences},
volume = {27},
doi = {10.1051/cocv/2021037},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2021037/}
}
TY - JOUR AU - Ferone, A. AU - Mercaldo, A. AU - Segura De León, S. TI - A singular elliptic equation and a related functional JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2021 VL - 27 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2021037/ DO - 10.1051/cocv/2021037 LA - en ID - COCV_2021__27_1_A41_0 ER -
%0 Journal Article %A Ferone, A. %A Mercaldo, A. %A Segura De León, S. %T A singular elliptic equation and a related functional %J ESAIM: Control, Optimisation and Calculus of Variations %D 2021 %V 27 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/cocv/2021037/ %R 10.1051/cocv/2021037 %G en %F COCV_2021__27_1_A41_0
Ferone, A.; Mercaldo, A.; Segura De León, S. A singular elliptic equation and a related functional. ESAIM: Control, Optimisation and Calculus of Variations, Tome 27 (2021), article no. 39. doi: 10.1051/cocv/2021037
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Cité par Sources :
The third author is partially supported by the Spanish Ministerio de Ciencia, Innovación y Universidades and FEDER, under project PGC2018–094775–B–I00. The first and second authors are partially supported by INdAM - GNAMPA
