A Variational Theory of Convolution-Type Functionals (Springerbriefs on Pdes and Data Science)

Alicandro, Roberto/ Ansini, Nadia/ Braides, Andrea

Springer Verlag, Singapore（2023/04発売）

• 製本 Paperback:紙装版/ペーパーバック版
• 言語 ENG
• 商品コード 9789819906840

Full Description

This book provides a general treatment of a class of functionals modelled on convolution energies with kernel having finite p-moments. A general asymptotic analysis of such non-local functionals is performed, via Gamma-convergence, in order to show that the limit may be a local functional representable as an integral. Energies of this form are encountered in many different contexts and the interest in building up a general theory is also motivated by the multiple interests in applications (e.g. peridynamics theory, population dynamics phenomena and data science). The results obtained are applied to periodic and stochastic homogenization, perforated domains, gradient flows, and point-clouds models.

This book is mainly intended for mathematical analysts and applied mathematicians who are also interested in exploring further applications of the theory to pass from a non-local to a local description, both in static problems and in dynamic problems.

 

Contents

Chapter 1. Introduction.- Chapter 2. Convolution-Type Energies.- Chapter 3. The Γ-limit of a Class of Reference Energies.- Chapter 4. Asymptotic Embedding and Compactness Results.- Chapter 5. A Compactness and Integral-Representation Result.- Chapter 6. Periodic Homogenization.- Chapter 7. A Generalization and Applications to Point Clouds.- Chapter 8. Stochastic Homogenization.- Chapter 9. Application to Convex Gradient Flows.