Sobolev Spaces of Vector-valued and Metric-valued Mappings
Analysis in metric spaces emerged at the end of the 90’s where various areas of Mathematics come together such as Functional Analysis, Differential Geometry, Geometric Measure Theory, Probability, PDEs or Complex Variables. One of the main purposes of this field is to understand what are the strictl...
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| Formato: | tesis doctoral |
| Fecha de publicación: | 2025 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/115160 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/115160 |
| Access Level: | acceso abierto |
| Palavra-chave: | 517.982.2(043.2) Espacios de Sobolev Matemáticas (Matemáticas) 12 Matemáticas |
| Resumo: | Analysis in metric spaces emerged at the end of the 90’s where various areas of Mathematics come together such as Functional Analysis, Differential Geometry, Geometric Measure Theory, Probability, PDEs or Complex Variables. One of the main purposes of this field is to understand what are the strictly necessary elements that make certain definitions and results work to develop analytical and geometric tools that can be applied in spaces that have little structure a priori, in this case, in a purely metric context. As indicated in the expository article [17], which describes current developments in Analysis in metric spaces, some of the main lines that have been developed so far in this area have been Poincaré inequalities in metric spaces, quasi-conformal maps, non-linear Potential Theory, differentiability of Lipschitz functions, certain bi-Lipschitz immersion theorems, Fractal Dynamics or Geometric Measure Theory in metric spaces, among others... |
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