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This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

The book presents a comprehensive exploration of curvilinear coordinates, emphasizing a direct proof of the three-dimensional Korn inequality. It delves into the nonlinear and linear equations by W.T. Koiter for modeling thin elastic shells, establishing the existence, uniqueness, and regularity of solutions through advanced mathematical concepts. Chapters 3 and 4 introduce differential geometry notions, enhancing the understanding of boundary value problems in elasticity and shell theory. The work is supported by research grants and references previous publications.

Focusing on the mathematical foundations of two-dimensional shell theory, this volume offers a comprehensive approach that avoids reliance on external references. It systematically presents the essential concepts and principles necessary for understanding the behavior and analysis of shells in engineering and physics, making it a valuable resource for students and professionals in these fields.

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.