抄録 This article discusses the Stokes equation in various classes of domains Ω CR n within
the L p-setting for 1≤ p≤∞ from the point of view of evolution equations. Classical as well …

Partial differential equations provide mathematical models of many important problems in
the physical sciences and engineering. This book treats one class of such equations …

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 …

Finite element exterior calculus is an approach to the design and understanding of finite
element discretizations for a wide variety of systems of partial differential equations. This …

In Chapter 1 we presented basic ideas for the reduction of boundary value problems of the
Laplacian to various forms of boundary integral equations based on the direct approach …

In this article we describe recent progress on the design, analysis and implementation of
hybrid numerical-asymptotic boundary integral methods for boundary value problems for the …

Periodic Homogenization of Elliptic Systems Page 1 Operator Theory Advances and
Applications 269 Zhongwei Shen Periodic Homogenization of Elliptic Systems Page 2 Page 3 …

The first two chapters contain introductory courses. Chapter 1 presents the theory of Sobolev-
type spaces Hs (s∈ R) on Rn, on a smooth closed manifold, and on a smooth bounded …

We study rates of convergence of solutions in L 2 and H 1/2 for a family of elliptic systems {L
_ ε\} with rapidly oscillating coefficients in Lipschitz domains with Dirichlet or Neumann …

We develop the theory of layer potentials and related singular integral operators as a tool to
study a variety of elliptic boundary problems on a family of domains introduced by Semmes …