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Home » HA Postdoc Seminar: Cauchy-Riemann systems for second order partial differential equations

Seminar

HA Postdoc Seminar: Cauchy-Riemann systems for second order partial differential equations March 14, 2017 (01:00 PM PDT - 02:00 PM PDT)
Parent Program:
Location: MSRI: Simons Auditorium
Speaker(s) Moritz Egert (Université de Paris XI)
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Complex analysis provides a well-known link between harmonic and holomorphic functions in the complex plane. Harmonicity is expressed by a single partial differential equation of second order, while holomorphy means solving the Cauchy-Riemann system consisting of two partial differential equations of first order. Over the last decades such a first-order approach has been developed for elliptic (and rather recently parabolic) equations in divergence form, the solution of the Kato square root problem being the starting point. In this informal talk I will try to explain main ideas of this approach. It gives rather algebraic translations of classical objects, questions, and results arising in the theory of these equations: solutions are described by semigroups, uniqueness corresponds to projection properties of spectral spaces, square function estimates follow from functional calculus. . . . This can already be fun in its own right but a particular strength of the approach is that it works equally well for equations with complex coefficients and does not rely on local regularity estimates for weak solutions.

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