Tullio Valent Livres

Focusing on local theorems of existence, uniqueness, and analytic dependence related to boundary value problems in finite elasticity, this book presents a systematic exploration of an n-dimensional generalization of three-dimensional elasticity. It emphasizes simultaneous local existence and uniqueness for compressible elastic bodies while excluding unilateral problems. The text builds on prior work, particularly the application of the inverse function theorem in hyperelasticity. The initial chapter introduces key concepts, while the second offers a technical framework for further developments.

The object of this book is the systematic exposition of recent work of the author's on boundary value problems of finite elasticity. These results concern an n-dimensional generalization of the three-dimensional elasticity which, aside from leading to a great many interesting mathematical situations, often shed light on certain aspects of the three-dimensional case. The book begins with a brief introduction to some general concepts, in order to show how the boundary value problems studied in the text arise. This is followed by the development of some technical material needed in the rest of the book. Subsequent chapters are devoted to obtaining theorems of existence, uniqueness and analytic dependence on the load, near special deformations for boundary value problems of place, and traction in finite elastostatics.