 | Seminario Matematico e Fisico di Milano |
| Alessandra Lunardi
Università di Parma
Sobolev and BV functions in infinite dimension
Venerdì 23 Febbraio 2018, ore 10:30 precise
Sala Consiglio, 7 piano, Edificio La Nave, Via Bonardi 9 |
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Abstract
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In Hilbert or Banach spaces $X$ endowed with a good probability measure $\mu$ there are a few "natural" definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals mainly with Gaussian measures and Sobolev and BV functions defined in the whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian measures, is largely to be developed.
As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an
infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations.
In this talk I will describe some of the main features and open problems concerning such function spaces.
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