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SUMMARY:Nonlinear Riemann-Hilbert Problems (continued) - Elias Wegert (Tec
 hnische Universität Bergakademie Freiberg)
DTSTART:20190924T130000Z
DTEND:20190924T140000Z
UID:TALK130618@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Nonlinear Riemann-Hilbert ProblemsElias Wegert\, TU Bergakadem
 ie Freiberg\, GermanyThough Bernhard Riemann&#39\;s thesis is commonly kno
 wn as the source of thecelebrated Riemann mapping theorem\, Riemann himsel
 f considered conformalmapping just as an example to illustrate his ideas a
 bout a more generalclass of nonlinear boundary value problems for analytic
  functions.The talks aim on making these Riemann-Hilbert problems more pop
 ular\, toencourage further research and to find novel applications.In the 
 first part we address the existence and uniqueness of solutionsfor differe
 nt problem classes and present two applications: potentialflow past a poro
 us object\, and a free boundary value problem inelectrochemical machining.
 In the second part\, a connection between Riemann-Hilbert problems and acl
 ass of extremal problems is established. Solutions to Riemann-Hilbertprobl
 ems are characterized by an extremal principle which generalizesthe classi
 cal maximum principle and Schwarz&#39\; lemma. We briefly sketch anapplica
 tion to the design of dynamical systems.In the end\, a class of nonlinear 
 transmission problems is considered.As a special result\, we obtain a hype
 rbolic version of the Riesz decompositionof functions on the unit circle i
 nto an analytic and an anti-analytic part.
LOCATION:Seminar Room 2\, Newton Institute
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