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Some fine properties of sets with finite perimeter in Wiener spaces

Michele Miranda Jr. — 2014

Banach Center Publications

In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...

Tyrosinase: a pleiotropic regulator by means of tyrosine level control and melanogenesis

Michele MirandaDario Botti — 1980

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Viene presentato un modello nel quale la tirosinasi occupa un ruolo centrale, come possibile regolatore della catecolaminosintesi, dell'assemblaggio dei microtubuli, della sintesi di tiroxina, della glicolisi e del ciclo dei pentosi fosfati, mediante una auto modulazione basata sul livello di tirosina e sulla produzione di melanina. Sono discusse possibili applicazioni del modello a condizioni normali e patologiche, come la fenilchetonuria, il parkinsonismo, la proliferazione dei melanociti e la...

Some Fine Properties of BV Functions on Wiener Spaces

Luigi AmbrosioMichele Miranda Jr.Diego Pallara — 2015

Analysis and Geometry in Metric Spaces

In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.

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