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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Nonlinear Riemann-Hilbert Problems (continued) - E
lias Wegert (Technische Universität Bergakademie F
reiberg)
DTSTART;TZID=Europe/London:20190924T140000
DTEND;TZID=Europe/London:20190924T150000
UID:TALK130618AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/130618
DESCRIPTION:Nonlinear Riemann-Hilbert ProblemsElias Wegert\, T
U Bergakademie Freiberg\, GermanyThough Bernhard R
iemann'\;s thesis is commonly known as the sour
ce of thecelebrated Riemann mapping theorem\, Riem
ann himself considered conformalmapping just as an
example to illustrate his ideas about a more gene
ralclass of nonlinear boundary value problems for
analytic functions.The talks aim on making these R
iemann-Hilbert problems more popular\, toencourage
further research and to find novel applications.I
n the first part we address the existence and uniq
ueness of solutionsfor different problem classes a
nd present two applications: potentialflow past a
porous object\, and a free boundary value problem
inelectrochemical machining.In the second part\, a
connection between Riemann-Hilbert problems and a
class of extremal problems is established. Solutio
ns to Riemann-Hilbertproblems are characterized by
an extremal principle which generalizesthe classi
cal maximum principle and Schwarz'\; lemma. We
briefly sketch anapplication to the design of dyna
mical systems.In the end\, a class of nonlinear tr
ansmission problems is considered.As a special res
ult\, we obtain a hyperbolic version of the Riesz
decompositionof functions on the unit circle into
an analytic and an anti-analytic part.
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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