Location:	Mantell Building
Email:	K.Zhang@sussex.ac.uk

Biography

Kewei Zhang's personal webpages

Research

Calculus of Variations, Systems of Nonlinear PDEs, Microstructure Weak Convergence methods.

My recent research includes the following topics: (i) existence of unstable solutions for a two-well variational model in the study of elastic material microstructure; (ii) the study of quasiconvex hulls and relations among semiconvex hulls in the calculus of variations; (iii) quasiconvex relaxation and effective moduli for specific models such as the multiwell problem; (iv) compensated compactness and Hardy spaces; (v) the coercivity problem for linear elliptic systems in 2D; (vi) instability of some models in computer vision; (vii) uniqueness problem for elliptic equations and systems in non-starshaped domains.

Future developments

These include:

1. General weak convergence methods in the calculus of variations and systems of PDEs. In particular, harmonic analysis methods and the effective use of the BMO space.

2. Separation of the gradient Young measure in the calculus of variations.

3. Explicit quasiconvex envelope and bounds for stored energy functions from the study of multiphase composites.

4. Dynamics of non-convex variational models.

5. Study of linear elliptic systems satisfying the Legendre-Hadamard ellipticity conditions.

Publications

On the Coercivity of Elliptic Systems in Two Dimensional Spaces Bull. Australian Math. Soc. 54, pp 423 - 430 (1996).

Compensated compactness, Hardy spaces and paracommutators (with C. Li, A. McIntosh, Z.-J. Wu ) J. Functional Anal. 150, pp 289 -306 (1997).

Quasiconvex Functions, SO(n) and Two Elastic Wells Ann. Inst. H. Poincaré - Anal.nonlinéaire 14, pp 759-785 (1997).

On various semiconvex hulls in the calculus of variations. Calc. Var. PDEs 6, pp 143-160 (1998).

On the structure of quasiconvex hulls Ann. Inst. H. Poincaré - Anal.nonlinéaire 15, pp 663-686 (1998)

Instability of the eikonal equation and shape from shading (with I. Barnes) M2AN Math. Model. Numer. Anal. 34, pp 127-138 (2000).

Uniqueness of solutions for some elliptic equations and systems in nearly star-shaped domains (with E. N. Dancer) Nonlinear Anal.41, pp 193-217 (2000).

A two-well structure and intrinsic mountain pass points Calc. Var. PDEs (to appear).