On the classical Reinforcement problem and Optimisation
Emanuele Cristoforoni, Carlo Nitsch, Cristina Trombetti
TL;DR
This survey reviews the classical reinforcement problem for elliptic boundary value problems, highlighting key contributions and related optimization issues from foundational papers by Sanchez-Palencia, Brezis, Caffarelli, Friedman, Acerbi, and Buttazzo.
Contribution
It provides a comprehensive overview of the classical reinforcement problem and discusses related optimization problems, emphasizing historical and theoretical developments.
Findings
Analysis of the reinforcement problem for elliptic PDEs
Discussion of optimization problems in the context of elliptic boundary value problems
Historical insights into foundational research by Sanchez-Palencia and others
Abstract
In the present survey, we consider the classical reinforcement problem for elliptic boundary value problems originally studied by Sanchez-Palencia in 1969. We focus on the seminar papers by Brezis, Caffarelli, & Friedman, and by Acerbi & Buttazzo, and discuss the related optimisation problems proposed by Friedman and by Buttazzo.
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Taxonomy
TopicsNonlinear Partial Differential Equations · Optimization and Variational Analysis · Nonlinear Differential Equations Analysis