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SUMMARY:Saugata Bandyopadhyay (IISER-Kolkata\, India)
DTSTART:20200929T093000Z
DTEND:20200929T103000Z
DTSTAMP:20260423T004656Z
UID:WOPARA/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WOPARA/3/">O
 n the Equation (∇u)^tH(u)(∇u) = G</a>\nby Saugata Bandyopadhyay (IISER
 -Kolkata\, India) as part of Webinar on PDE and related areas\n\n\nAbstrac
 t\nLet n∈N\,n>2 and let Ω⊆R^n be open.  Let H\, G:R^n→R^{n×n} be 
 of appropriate regularity.  We discuss the existence of an immersionu: Ω
 →R^n of appropriate regularity\, satisfying (∇u)^tH(u)(∇u) =G in Ω
 ......(1)\n\nWe consider Cauchy\, Dirichlet and Dirichlet-Neumann problems
 .Equation (1) comes up in diverse contexts.  WhenH(and henceG) issymmetric
  and positive definite\, Equation (1) is connected to the prob-lem of equi
 valence of Riemannian metrics.  The symmetric case is alsoimportant in the
  non-linear elasticity theory because of its connectionwith the Cauchy-Gre
 en deformation tensor.  WhenH(and henceG) isskew-symmetric\, Equation (1) 
 comes up in the context of the problemof equivalence of differential two-f
 orms.The aim of the talk is to present a survey of recent progress and ad-
 vances made in the context of Equation (1).  We shall also discuss thegene
 ral case whenH\,Gare neither symmetric nor skew-symmetric.\n
LOCATION:https://researchseminars.org/talk/WOPARA/3/
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