EmbedDirichlet (274519)

  https://cordis.europa.eu/project/id/274519

  FP7 (2007-2013)

  Embeddings of weighted Sobolev spaces and applications to Dirichlet problems

  Marie-Curie Action: "Intra-European fellowships for career development" (FP7-PEOPLE-2010-IEF)

  partial differential equations

  2012-02-15 Start Date (YY-MM-DD)

  2014-02-14 End Date (YY-MM-DD)

  € 185,362 Total Cost

  Description

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.

  Complicit Organisations

1 Israeli organisation participates in EmbedDirichlet.