| Full text | |
| Author(s): |
Chata, Juan Carlos Ortiz
;
Pimenta, Marcos T. O.
;
Leon, Sergio Segura de
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Mathematical Analysis and Applications; v. 525, n. 2, p. 25-pg., 2023-03-06. |
| Abstract | |
In this paper, we analyze a "concave-convex" type problem involving the 1-Laplacian operator in a general Lipschitz-continuous domain and prove the existence of two positive solutions. Owing to 1-Laplacian is 0-homogeneous, the "concave" term must be singular. Hence, we should deal with an energy functional having two non- differentiable terms: the total variation and that one coming from the singular term. Due to these difficulties, we do not get solutions as critical points of the energy functional defined in the BV(omega) space. Instead, we study problems involving the p-Laplacian operator and let p go to 1.(c) 2023 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 21/04158-4 - Elliptic problems involving the mean-curvature operator in the space of functions of bounded variation |
| Grantee: | Marcos Tadeu de Oliveira Pimenta |
| Support Opportunities: | Regular Research Grants |
| FAPESP's process: | 19/13503-7 - Weighted quasilinear elliptic problems in the space of functions of bounded variation |
| Grantee: | Juan Carlos Ortiz Chata |
| Support Opportunities: | Scholarships abroad - Research Internship - Doctorate |
| FAPESP's process: | 17/06119-0 - Quasilinear elliptic problems in the space of functions of bounded variation |
| Grantee: | Juan Carlos Ortiz Chata |
| Support Opportunities: | Scholarships in Brazil - Doctorate |