Publisher Summary This chapter provides an overview of the recent developments
concerning Saint-Venant's principle. The task of determining, within the framework of the …

Korn's inequalities have played a central role in the development of linear elasticity, not only
in connection with the basic theoretical issues such as existence and uniqueness, but also …

This series of books forms a unique and rigorous treatise on various mathematical aspects
of fluid mechanics models. These models consist of systems of nonlinear partial differential …

The book provides a comprehensive, detailed and self-contained treatment of the
fundamental mathematical properties of boundary-value problems related to the Navier …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This book presents an account of theories of? ow in porous media which have proved
tractable to analysis and computation. In particular, the t-ories of Darcy, Brinkman, and …

Saint-Venant's principle plays a central role in the theory and applications of elasticity. A
comprehensive review of contemporary research on this topic was given by Horgan and …

In unbounded domains Ω of the three-dimensional Euclidean space, having several outlets
Ω ii= 1,..., N, at infinity, one investigates the time-dependent solutions of the Stokes and …

KORN'S inequalities for integrals of quadratic functionals subject to certain side conditions
have played a fundamental role in the development of elasticity theory (see eg [I-14]). The …

Liouville-type theorems for the steady incompressible Navier-Stokes system are investigated
for solutions in a three-dimensional slab with either no-slip boundary conditions or periodic …