Surjection and inversion for locally Lipschitz maps between Banach spaces
We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdi...
| Autores: | , |
|---|---|
| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/12888 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/12888 |
| Access Level: | acceso abierto |
| Palabra clave: | 517.98 Global invertibility Palais-Smale condition Nonsmooth analysis Análisis funcional y teoría de operadores |
| Sumario: | We study the global invertibility of non-smooth, locally Lipschitz maps between infinite-dimensional Banach spaces, using a kind of Palais-Smale condition. To this end, we consider the Chang version of the weighted Palais-Smale condition for locally Lipschitz functionals in terms of the Clarke subdifferential, as well as the notion of pseudo-Jacobians in the infinite-dimensional setting, which are the analog of the pseudo-Jacobian matrices defined by Jeyakumar and Luc. Using these notions, we derive our results about existence and uniqueness of solution for nonlinear equations. In particular, we give a version of the classical Hadamard integral condition for global invertibility in this context. |
|---|