At the Edge of Ellipticity
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Organizer(s): |
Name:
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Affiliation:
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Country:
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Fabiana Leoni
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Sapienza Università di Roma
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Italy
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Isabeau Birindelli
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Sapienza Università di Roma
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Italy
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Sergio Polidoro
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Università di Modena e Reggio Emilia
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Italy
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Abstract:
| | Diffusive phenomena are described through elliptic equations and typically the diffusive term is represented by the Laplacian that corresponds to a uniform diffusion. This needs not be the case, for instance diffusion can happen along fixed directions: “in the black death epidemic, contagion advanced along roads and from there spread inwards leading to a front like invasion of Western Europe roughly from South to North”, and “this effect of roads still matters” in modern epidemics, as COVID-19 shows, [BRR].
Weakening the notion of ellipticity allows a more effective description of the reality, as occurs in models of mathematical finance, kinetic theory, mathematical physics, and engineering. In this Session we plan to tackle several problems that lie “at the edge of ellipticity”. Of course this “edge” is very vast, we will focus on:
- subelliptic operators,
- fully nonlinear operators,
- higher order operators.
The concept of degeneracy serves as a bridge between the known phenomena typical of uniformly elliptic equations, and the development of new mathematical ideas needed to shed some light on some very unusual properties of degenerate PDEs. |
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List of approved abstract |
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