Artículos de revistas
Anisotropic 1-Laplacian problems with unbounded weights
Fecha
2021-12-01Registro en:
Nonlinear Differential Equations and Applications, v. 28, n. 6, 2021.
1420-9004
1021-9722
10.1007/s00030-021-00717-4
2-s2.0-85112806623
Autor
Universidade Estadual Paulista (UNESP)
Universitat de València
Institución
Resumen
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.