This classic text focuses on elliptic boundary value problems in domains with nonsmooth boundaries and on problems with mixed boundary conditions. Its contents are essential for an understanding of the behavior of numerical methods for partial differential equations (PDEs) on two-dimensional domains with corners. Elliptic Problems in Nonsmooth Domains provides a careful and self-contained development of Sobolev spaces on nonsmooth domains, develops a comprehensive theory for second-order elliptic boundary value problems and addresses fourth-order boundary value problems and numerical treatment of singularities. This book is intended for researchers and graduate students in computational science and numerical analysis who work with theoretical and numerical PDEs. Readers need only a background in functional analysis to find the material accessible.