The term "weakly differentiable functions" in the title refers to those inte- n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func- tions), have undergone considerable development during the past 20 years....
The term "weakly differentiable functions" in the title refers to those inte- n grable functions defined on an open subset of R whose partial derivati...
The term "weakly differentiable functions" in the title refers to those inte- n grable functions defined on an open subset of R whose partial derivatives in the sense of distributions are either LP functions or (signed) measures with finite total variation. The former class of functions comprises what is now known as Sobolev spaces, though its origin, traceable to the early 1900s, predates the contributions by Sobolev. Both classes of functions, Sobolev spaces and the space of functions of bounded variation (BV func- tions), have undergone considerable development during the past 20 years....
The term "weakly differentiable functions" in the title refers to those inte- n grable functions defined on an open subset of R whose partial derivati...
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is...
This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a d...
