Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

Essays suggest or explore reasons why violent acts might have been perpetrated, and attempt to understand the social priorities which governed such acts. Thought-provoking and characterized by a high level of scholarship. HISTORYAn important addition to the dialogue concerning the nature of conflict and its resolution in the early medieval West. HISTORIAN [US] The `violence' oflife in the middle ages is nowadays both taken for granted and little understood. The essays in this collection all suggest or explore reasons why violent acts might have been perpetrated, and attempt to understand the social priorities which governed such acts. Broadly, the studies clarify issues relating to the creation of political identities and the establishment of social order, and cover matters of administration, religious ritual, and gender.Contributors: GUY HALSALL, LUIS A. GARCIA MORENO, PAUL FOURACRE, T.S. BROWN, JANET L. NELSON, N.B. AITCHISON, MATTHEW BENNETT, GUY A.E. MORRIS, S.J. SPEIGHT, ROSS BALZARETTI, JULIE COLEMAN, NANCY L. WICKER. GUY HALSALL is lecturer in the Department of History, Birkbeck College, University of London. Contributors: GUY HALSALL, LUIS A. GARCIA MORENO, PAUL FOURACRE, T.S. BROWN, JANET L. NELSON, N.B. AITCHISON, MATTHEW BENNETT, GUY A.E. MORRIS, S.J. SPEIGHT, ROSS BALZARETTI, JULIE COLEMAN, NANCY L. WICKER.