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Topological Degree and Variational Methods, with Applications to the Problem of Bubbles with Prescribed Mean Curvarture

Course Type: 
PhD Course
Academic Year: 
2012-2013
Period: 
March-May
Duration: 
60 h
Description: 
  • Degree theory:
    • Topological approach to finite-dimensional problems.
    • Sard's Theorem.
    • Finite dimensional degree theory and the Brouwer fixed point theorem.
    • Topological degree in infinite-dimensional Banach spaces.
    • The Schauder fixed-point theorem.
  • Application to the H-bubble problem:
    • Preliminaries on the H-bubble problem: the mean curvature of a radial graph in Rn over the unit sphere.
    • Existence results from Treibergs-Wei [J.Diff.Geom. 1983], Gerhardt [J.Diff.Geom. 1988],¬†Caldiroli-Gullino [J. Fix. Point Theory Appl.], to appear.
    • The case n=2: the variational approach to the H-loops problem for circles in R2: an existence result via min-max and degree arguments.
  • Further applications to semilinear nonlinear differential equations will be presented, depending on students' interests and time availability.
Location: 
A-133
Next Lectures: 

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