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curvilinear coordinates. This remedy contains specifically a right away facts of the three-d Korn inequality in curvilinear coordinates. The fourth and final bankruptcy, which seriously depends on bankruptcy 2, starts off through an in depth description of the nonlinear and linear equations proposed through W.T. Koiter for modeling skinny elastic shells. those equations are “two-dimensional”, within the feel that they're expressed when it comes to curvilinear coordinates used for de?ning the center floor of the shell. The life, strong point, and regularity of ideas to the linear Koiter equations is then verified, thank you this time to a primary “Korn inequality on a floor” and to an “in?nit- imal inflexible displacement lemma on a surface”. This bankruptcy additionally contains a short creation to different two-dimensional shell equations. curiously, notions that pertain to di?erential geometry in step with se,suchas covariant derivatives of tensor ?elds, also are brought in Chapters three and four, the place they seem so much clearly within the derivation of the fundamental boundary worth difficulties of third-dimensional elasticity and shell idea. sometimes, parts of the fabric coated listed below are tailored from - cerpts from my booklet “Mathematical Elasticity, quantity III: idea of Shells”, released in 2000by North-Holland, Amsterdam; during this appreciate, i'm indebted to Arjen Sevenster for his type permission to depend upon such excerpts. Oth- clever, the majority of this paintings was once considerably supported via delivers from the study provides Council of Hong Kong specified Administrative sector, China [Project No. 9040869, CityU 100803 and undertaking No. 9040966, CityU 100604].