Vectorial Elliptic, Parabolic and Variational Prob.. (VECTORIAL PROBLEMS)
Vectorial Elliptic, Parabolic and Variational Problems: Singularities and Regularity
Start date: Jul 1, 2008,
End date: Jun 30, 2013
The aim of the proposed project is to start a systematic investigation of the fine regularity and singularity properties of solutions to vectorial problems, of elliptic and parabolic type, with special emphasis on the ones admitting a variational structure. A distinguishing feature of vectorial problems is the possibility of having solutions with singularities; in turn the structure of such singularities encodes subtle information about the fundamental nature of the underlying problem. Analytic, geometric and topological phenomena concur in the formation and in the nature of the singularities observed, and the analysis of the singular sets requires a very high interaction of several different methods and techniques coming from different branches of Mathematics. Unraveling the singular sets structure is of paramount importance to clarify the basic nature of the mathematical phenomena considered; specifically, it can allow for their efficient numerical treatment, and for using them in the context of mathematical modeling, towards the applications in Science.
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