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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.
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