Yann Bernard

Dr

20062020

Research activity per year

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Personal profile

Biography

B.S. in Mathematics from the University of Michigan, USA (2000)

Ph.D. in Mathematics from the University of Michigan, USA (2006)

Research postdoc at the ETHZ in Zurich, Switzerland (2006-2009 and 2014-2015)

Research fellow at the Albert-Ludwigs-Universitaet in Freiburg, Germany (2009-2014)

Research interests

My research deals with analyzing problems coming from the geometry of elastic surfaces, and which model, for examples, the shape of red blood cells and of liposome vesicles. Typically, an energy involving geometric quantities (e.g. the mean curvature of a surface) is to be minimized. Its critical points satisfy a nonlinear system of fourth order elliptic PDEs. I am concerned with studying the analytical properties of the solutions to such systems (e.g. regularity, asymptotic behavior near singularities, compactness/convergence of sequences of solutions, etc…). One major difficulty with fourth-order problems is that, unlike second-order problems, their solutions do not satisfy any maximum principle. Handling the nonlinearities is also a delicate matter that requires working with functional spaces more 'exotic' than the ones commonly found (e.g. Hardy spaces, Lorentz spaces). Want to more? Have a look at my webpage (users.monash.edu.au/~byann) or stop by my office (B28, Rm 421) and ask!

 

Areas of expertise: functional analysis, harmonic analysis, geometric analysis, elliptic and parabolic PDEs, variational calculus.

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