@book{f84349c5365b406aa34a2b9b8ecef682,

title = "Partial Differential Equations: A Unified Hilbert Space Approach",

abstract = "This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev Lattice structure, a simple extension of the well established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space (rather than an apparently more general Banach space) setting is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations which consider either specific types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics. ",

keywords = "mathematics, partial differential , equations, Hilbert space, Sobolev, evolution equation",

author = "Desmond Mcghee and R. Picard",

note = "e-isbn: 978-3-11-025027-5",

year = "2011",

month = jun,

day = "16",

language = "English",

isbn = "9783110250275",

series = "de Gruyter Expositions in Mathematics 55 ",

publisher = "de Gruyter",

}