Computational Methods for Variational Problems

Research - Groups

• Statistical Analysis and Computation Methods and Stochastic Models
• Symmetry/Integrability Analysis and Computer Algebra for Nonlinear Differential Equations
• Computational Methods for Variational Problems
• Analysis and Simulation of Discrete, Spatially-extended Dynamical Systems
• Computational Algebra and Number Theory
• Computer Algebra Algorithms and Parallel Computing
• Computational Topics in General Relativity, Gauge Theory, Classical Mechanics

Computational Methods for Variational Problems

H. Ben-El-Mechaiekh has published extensively in the field of Nonlinear Functional Analysis and applications and is an expert in fixed point theory and the solvability of nonlinear problems. R. Kerman has written a number of papers in the areas of Fourier Analysis and Approximation Theory. For the past ten years he has been involved in research on Sobolev and Besov spaces and is a principal investigator of a NATO group, currently working on some applications to problems in nonlinear PDEs with rapidly increasing coefficients.

Representative publications

1. H. Ben-El-Mechaiekh (with S. Chebbi, M. Florenzano), Generalized KKM Principle and Applications, Journal of Math. Analysis and Applications, in print.
2. H. Ben-El-Mechaiekh, “Spaces and Maps Approximations and Fixed Points, Special issue on Fixed Point Theory and Applications”, Journal of Computational and Applied Mathematics 113 (2000), 283-308 (invited contribution).
3. H. Ben-EI-Mechaiekh (withG. Isac), “Generalized multivalued variational inequalities”, in Topology and Analysis, Volume dedicated to Professor S. Stoilow, C. Andreian-Cazacu, O. Letho and T.M. Rassias, Eds., World Scientific Publishing Co. (1998), 115-142.
4. H. Ben-El-Mechaiekh (with W. Kryszewski), “Equilibria for set-valued maps on nonconvex domains”, Transactions of the American Math. Soc. 349 (1997), 4159-4179.
5. R. Kerman (with M.L. Huang and Y. Weit), “Abel summability of the autoregressive series for the best linear least squares predictor” ,Illinois J. Math 41 (1997),577-588.
6. R. Kerman (with M. Goldman), “On optimal embedding of Calderon spaces and Besov spaces”, Proceedings of the Steklov Institue,Spring 2004.
7. R. Kerman (with L. Pick), “Optimal Sobolev imbeddings”, Forum Mathematicum, to appear.