Research Output per year

## 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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## Research Output 2006 2019

- 10 Article

## Uniform regularity results for critical and subcritical surface energies

Bernard, Y. & Rivière, T., 1 Feb 2019, In : Calculus of Variations and Partial Differential Equations. 58, 1, 39 p., 10.Research output: Contribution to journal › Article › Research › peer-review

## Rigidity and stability of spheres in the Helfrich model

Bernard, Y., Wheeler, G. & Wheeler, V. M., 15 Jan 2018, In : Interfaces and Free Boundaries. 19, 4, p. 495-523 29 p.Research output: Contribution to journal › Article › Research › peer-review

## Analysis of constrained Willmore surfaces

Bernard, Y., 2 Oct 2016, In : Communications in Partial Differential Equations. 41, 10, p. 1513-1552 40 p.Research output: Contribution to journal › Article › Research › peer-review

## Noether's theorem and the Willmore functional

Bernard, Y., 1 Jul 2016, In : Advances in Calculus of Variations. 9, 3, p. 217-234 18 p.Research output: Contribution to journal › Article › Research › peer-review

## Energy quantization for Willmore surfaces and applications

Bernard, Y. & Riviere, T., 2014, In : Annals of Mathematics. 180, 1, p. 87 - 136 50 p.Research output: Contribution to journal › Article › Research › peer-review