curvilinear coordinates. This treatment includes in particular a direct
proof of the three-dimensional Korn inequality in curvilinear
coordinates. The fourth and last chapter, which heavily relies on
Chapter 2, begins by a detailed description of the nonlinear and linear
equations proposed by W.T. Koiter for modeling thin elastic shells.
These equations are "two-dimensional", in the sense that they are
expressed in terms of two curvilinear coordinates used for de?ning the
middle surface of the shell. The existence, uniqueness, and regularity
of solutions to the linear Koiter equations is then established, thanks
this time to a fundamental "Korn inequality on a surface" and to an
"in?nit- imal rigid displacement lemma on a surface". This chapter also
includes a brief introduction to other two-dimensional shell equations.
Interestingly, notions that pertain to di?erential geometry per se,
suchas covariant derivatives of tensor ?elds, are also introduced in
Chapters 3 and 4, where they appear most naturally in the derivation of
the basic boundary value problems of three-dimensional elasticity and
shell theory. Occasionally, portions of the material covered here are
adapted from - cerpts from my book "Mathematical Elasticity, Volume III:
Theory of Shells", published in 2000by North-Holland, Amsterdam; in this
respect, I am indebted to Arjen Sevenster for his kind permission to
rely on such excerpts. Oth- wise, the bulk of this work was
substantially supported by two grants from the Research Grants Council
of Hong Kong Special Administrative Region, China [Project No. 9040869,
CityU 100803 and Project No. 9040966, CityU 100604].
