This book is the second of a set dedicated to the mathematical tools used in partial differential equations derived from physics.
It presents the properties of continuous functions, which are useful for solving partial differential equations, and, more particularly, for constructing distributions valued in a Neumann space.
The author examines partial derivatives, the construction of primitives, integration and the weighting of value functions in a Neumann space. Many of them are new generalizations of classical properties for values in a Banach space.
Simple methods, semi-norms, sequential properties and others are discussed, making these tools accessible to the greatest number of students – doctoral students, postgraduate students – engineers and researchers, without restricting or generalizing the results.
1. Spaces of Continuous Functions.
2. Differentiable Functions.
3. Differentiating Composite Functions and Others.
4. Integrating Uniformly Continuous Functions.
5. Properties of the Measure of an Open Set.
6. Additional Properties of the Integral.
7. Weighting and Regularization of Functions.
8. Line Integral of a Vector Field Along a Path.
9. Primitives of Continuous Functions.
10. Additional Results: Integration on a Sphere.
Jacques Simon is Honorary Research Director at CNRS. His research focuses on Navier-Stokes equations, particularly in shape optimization and in the functional spaces they use.
Table of Contents
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