Cargando…
Sobolev spaces on metric measure spaces : an approach based on upper gradients /
Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of m...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2015.
|
| Colección: | New mathematical monographs ;
27. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Introduction
- Review of basic functional analysis
- Lebesgue theory of Banach space-valued functions
- Lipschitz functions and embeddings
- Path integrals and modulus
- Upper gradients
- Sobolev spaces
- Poincaré inequalities
- Consequences of Poincaré inequalities
- Other definitions of Sobolev-type spaces
- Gromov-Hausdorff convergence and Poincaré inequalities
- Self-improvement of Poincaré inequalities
- An introduction to Cheeger's differentiation theory
- Examples, applications, and further research directions.