From De Giorgi to Hormander and back to Boltzmann...
【2018.9.8 4:00pm, N202】 |
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2018-9-7
Colloquia & Seminars
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Speaker
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Prof. Clement Mouhot, University of Cambridge, UK
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Title
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From De Giorgi to Hormander and back to Boltzmann...
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Time
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September 8, 4:00-5:00pm, 2018
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Venue
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N202
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Abstract
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We will discuss recent results and a new line of research at the crossroad of two major theories in the analysis of partial differential equations. The celebrated De Giorgi-Nash-Moser theorem provides Holder continuity and Harnack inequality for uniformly elliptic equations with rough coefficients (in divergence form). The theory of hypoellipticity of Hormander provides general “bracket” conditions for regularity of solutions to partial differential equations combining first and second order derivative operators when ellipticity fails in some directions. We discuss recent extensions of the De Giorgi-Nash-Moser theory to hypoelliptic equations of kinetic type with rough coefficients. We then discuss applications to the Boltzmann and Landau equations in kinetic theory and present a program of research with some answers and many open questions.
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Affiliation
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Invited Speaker at the ICM Rio 2018
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