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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Weakly Differentiable Functions - Sobolev Spaces and Functions of Bounded Variation (Hardcover, 1989 ed.)
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Weakly Differentiable Functions - Sobolev Spaces and Functions of Bounded Variation (Hardcover, 1989 ed.)
Series: Graduate Texts in Mathematics, 120
Expected to ship within 12 - 17 working days
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The major thrust of this book is the analysis of pointwise behavior
of Sobolev functions of integer order and BV functions (functions
whose partial derivatives are measures with finite total
variation). The development of Sobolev functions includes an
analysis of their continuity properties in terms of Lebesgue
points, approximate continuity, and fine continuity as well as a
discussion of their higher order regularity properties in terms of
Lp-derivatives. This provides the foundation for further results
such as a strong approximation theorem and the comparison of Lp and
distributional derivatives. Also included is a treatment of
Sobolev-PoincarA(c) type inequalities which unifies virtually all
inequalities of this type. Although the techniques required for the
discussion of BV functions are completely different from those
required for Sobolev functions, there are similarities between
their developments such as a unifying treatment of PoincarA(c)-type
inequalities for BV functions. This book is intended for graduate
students and researchers whose interests may include aspects of
approximation theory, the calculus of variations, partial
differential equations, potential theory and related areas. The
only prerequisite is a standard graduate course in real analysis
since almost all of the material is accessible through real
variable techniques.
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