| Full text | |
| Author(s): |
Total Authors: 3
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| Affiliation: | [1] Univ Estadual Paulista UNESP, Inst Biociencias Letras & Ciencias Exatas, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil
[2] Univ Estadual Paulista Unesp, Fac Ciencias & Tecnol, Dept Matemat & Computacao, BR-19060900 Presidente Prudente, SP - Brazil
[3] Univ Valencia, Dept Anal Matemat, Valencia 46100 - Spain
Total Affiliations: 3
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| Document type: | Journal article |
| Source: | NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS; v. 28, n. 6 DEC 2021. |
| Web of Science Citations: | 0 |
| Abstract | |
In this work we prove the existence of nontrivial bounded variation solutions to quasilinear elliptic problems involving a weighted 1-Laplacian operator. A key feature of these problems is that weights are unbounded. One of our main tools is the well-known Caffarelli-Kohn-Nirenberg's inequality, which is established in the framework of weighted spaces of functions of bounded variation (and that provides us the necessary embeddings between weighted spaces). Additional tools are suitable variants of the Mountain Pass Theorem as well as an extension of the pairing theory by Anzellotti to this new setting. (AU) | |
| FAPESP's process: | 19/14330-9 - Variational and nonvariational elliptic problems involving the 1-Laplacian operator |
| Grantee: | Marcos Tadeu de Oliveira Pimenta |
| Support Opportunities: | Regular Research Grants |
| 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 |
| 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 |