The classical approach of solving calculus of variations problems resorts to the Euler-Lagrange Equations, which are in general a system of higher order nonlinear differential equations and is in general very difficult to tackle. For certain types of variational problems, the use of suitably devised integral inequalities could lead to optimal solutions effectively without having to consider the Euler- Lagrange Equations. A few examples of this approach will be given in this talk.

Wing-Sum Cheung is a full Professor of the Department of Mathematics of the University of Hong Kong. He holds a B.Sc. (with 1st class honors) from the Chinese University of Hong Kong, a M.A. and a Ph.D. from Harvard University, USA. He had been the Head of Department of Mathematics and Associate Dean (Development and External Relations) of the Faculty of Science of the University of Hong Kong, Vice-President of the Hong Kong Mathematical Society, Council Member of the Southeast Asian Mathematical Society, Council Member of the Hong Kong Institute of Science, Leader of the Hong Kong International Olympiad Team, and an Honorary Consultant of the Ministry of Education, Youth and Sports of the Government of Cambodia. He has published over 200 journal articles, conference proceedings and book chapters, in which over 140 are published in ISI journals. He has been named Top 1% Researcher in the world by Clarivate Analytics’ Essential Science Indicator 6 times in the last decade. He is on the editorial board of a number of international mathematical journals including Asian European Journal of Mathematics, Australian Journal of Mathematical Analysis and Applications, Bulletin of the Southeast Asian Mathematical Society, Far East Journal of Mathematical Sciences, Journal of Inequalities and Applications, etc. His current research interests include Differential Geometry, Exterior Differential Systems, Calculus of Variations, Analytic Inequalities, and Differential Equations.