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Pattern formation, optimal transport and interpolation inequalities

Connections for Women on Optimal Transport: Geometry and Dynamics August 22, 2013 - August 23, 2013

August 23, 2013 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Eleonora Cinti (Università di Bologna)
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


Abstract In this talk I will present some interpolation inequalities which arise in the study of pattern formation in physics. In many physical problems described by a variational model (such as domain branching in ferromagnets, superconductors, twin branching in shape memory alloys), the energy is given by the competition of two main terms: an interfacial energy (described by a BV-norm) and a transport term (described by a negative norm or a Wasserstein distance). In order to establish a rigorous lower bound for the energy of minimizing configurations, one needs suitable interpolation inequalities. I will describe the connection between these interpolation estimates and the physical problem, and I will sketch the proof of some of these estimates. This is a joint work with Felix Otto.
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