BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Sabre//Sabre VObject 4.5.8//EN CALSCALE:GREGORIAN BEGIN:VTIMEZONE TZID:Europe/Zurich X-LIC-LOCATION:Europe/Zurich TZURL:http://tzurl.org/zoneinfo/Europe/Zurich BEGIN:DAYLIGHT TZOFFSETFROM:+0100 TZOFFSETTO:+0200 TZNAME:CEST DTSTART:19810329T020000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZOFFSETFROM:+0200 TZOFFSETTO:+0100 TZNAME:CET DTSTART:19961027T030000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT UID:news277@dmi.unibas.ch DTSTAMP;TZID=Europe/Zurich:20180716T232119 DTSTART;TZID=Europe/Zurich:20130419T110000 SUMMARY:Seminar in Numerical Analysis: Wolfgang Wendland (Universität Stut tgart) DESCRIPTION:As a special case of nonlinear Rieman--Hilbert problems with cl osed boundary data in multiply connected domains\, here a doubly connecte d domain like an annulus is considered.\\r\\nThe nonlinear boundary cond itions for the desired holomorphic solutions lead to nonlinear singular i ntegral equations on the boundary which belong to the class of quasiruled Fredholm maps defined on quasicylindrical domains in appropriate separab le Banach spaces.\\r\\nThe closed boundary data give a priori estimates f or the modulus of solutions which in turn implies a priori estimates in t he Sobolev spaces considered here. For this class of problems\, the Shnir elman--Efendiev degree of mappings can be defined which allows to investi gate the existence of solutions if the boundary conditions satisfy some t opological assumptions.\\r\\nThe lifting of the boundary  value problem via holomorphic transformation onto the universal covering of the unit di sc allows to construct a homotopic deformation of the lifted nonlinear si ngular integral equations to a uniquely solvable case  which implies tha t the degree of mapping is 1 and existence of (in fact at least two) solu tions follows.\\r\\nIf the nonlinear integral equations on the boundary a re appoximated by trigonometric point collocation then the theory also i mplies that approximate solutions exist and converge asymptotically. X-ALT-DESC:As a special case of nonlinear Rieman--Hilbert problems with clo sed boundary data in multiply connected domains\, here a doubly connected domain like an annulus is considered.\nThe nonlinear boundary condition s for the desired holomorphic solutions lead to nonlinear singular integr al equations on the boundary which belong to the class of quasiruled Fred holm maps defined on quasicylindrical domains in appropriate separable Ba nach spaces.\nThe closed boundary data give a priori estimates for the mo dulus of solutions which in turn implies a priori estimates in the Sobole v spaces considered here. For this class of problems\, the Shnirelman--Ef endiev degree of mappings can be defined which allows to investigate the existence of solutions if the boundary conditions satisfy some topologica l assumptions.\nThe lifting of the boundary \; value problem via holo morphic transformation onto the universal covering of the unit disc allow s to construct a homotopic deformation of the lifted nonlinear singular i ntegral equations to a uniquely solvable case \; which implies that t he degree of mapping is 1 and existence of (in fact at least two) solutio ns follows.\nIf the nonlinear integral equations on the boundary are app oximated by trigonometric point collocation then the theory also implies that approximate solutions exist and converge asymptotically. DTEND;TZID=Europe/Zurich:20130419T120000 END:VEVENT END:VCALENDAR