EMBEDDIRICHLET
Embeddings of weighted Sobolev spaces and applications to Dirichlet problems
| Coordinatore | BEN-GURION UNIVERSITY OF THE NEGEV
Organization address
address: Office of the President - Main Campus contact info |
| Nazionalità Coordinatore | Israel [IL] |
| Totale costo | 185˙362 € |
| EC contributo | 185˙362 € |
| Programma | FP7-PEOPLE
Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) |
| Code Call | FP7-PEOPLE-2010-IEF |
| Funding Scheme | MC-IEF |
| Anno di inizio | 2012 |
| Periodo (anno-mese-giorno) | 2012-02-15 - 2014-02-14 |
Partecipanti
| # | ||||
|---|---|---|---|---|
| 1 |
BEN-GURION UNIVERSITY OF THE NEGEV
Organization address
address: Office of the President - Main Campus contact info |
IL (BEER SHEVA) | coordinator | 185˙362.40 |
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Obiettivo del progetto (Objective)
'Sobolev spaces were introduced as solution spaces of elliptic partial differential equations. The theoretical study of Sobolev spaces is mainly motivated by the applications to the resolution of partial differential equations. Weighted Sobolev spaces allow to solve degenerate partial differential equations. In this respect, compact embeddings of Sobolev spaces play a crucial role. In recent works, V. Gol'dshtein and A. Ukhlov obtained compact embedding properties for weighted Sobolev spaces, considering domains which are homeomorphic images of a smooth bounded domain via mappings from a certain class, called weighted quasiconformal mappings (or mappings with bounded mean distorsion). In this project, we plan to study several degenerate partial differential equations involving Dirichlet conditions. To do this, we will introduce a double-weighted Sobolev space, which is more appropriate with respect to the considered type of nonlinear equations. We will first study the abstract, analytic properties of this new nonstandard class of spaces. Then, we will study their embeddings in a Lebesgue space, also using the relatively new theory of weighted quasiconformal mappings. Finally, we will apply these abstract results in order to construct solutions of boundary value problems for the elliptic equations we consider.'