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SUMMARY:Nonlinear Riemann-Hilbert Problems (continued) - Elias Wegert (Tec
 hnische Universität Bergakademie Freiberg)
DTSTART:20190924T130000Z
DTEND:20190924T140000Z
UID:TALK130615@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Nonlinear Riemann-Hilbert Problems<br><br>Elias Wegert\, TU Be
 rgakademie Freiberg\, Germany<br><br>Though Bernhard Riemann&#39\;s thesis
  is commonly known as the source of the<br>celebrated Riemann mapping theo
 rem\, Riemann himself considered conformal<br>mapping just as an example t
 o illustrate his ideas about a more general<br>class of nonlinear boundary
  value problems for analytic functions.<br>The talks aim on making these R
 iemann-Hilbert problems more popular\, to<br>encourage further research an
 d to find novel applications.<br><br>In the first part we address the exis
 tence and uniqueness of solutions<br>for different problem classes and pre
 sent two applications: potential<br>flow past a porous object\, and a free
  boundary value problem in<br>electrochemical machining.<br><br>In the sec
 ond part\, a connection between Riemann-Hilbert problems and a<br>class of
  extremal problems is established. Solutions to Riemann-Hilbert<br>problem
 s are characterized by an extremal principle which generalizes<br>the clas
 sical maximum principle and Schwarz&#39\; lemma. We briefly sketch an<br>a
 pplication to the design of dynamical systems.<br>In the end\, a class of 
 nonlinear transmission problems is considered.<br>As a special result\, we
  obtain a hyperbolic version of the Riesz decomposition<br>of functions on
  the unit circle into an analytic and an anti-analytic part.
LOCATION:Seminar Room 2\, Newton Institute
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