Calculus of Variations and Geometric Measure Theory

G. Buttazzo - J. Casado-Diaz - F. Maestre

Optimal coefficients for elliptic PDEs

created by buttazzo on 15 Jul 2024

[BibTeX]

Preprint

Inserted: 15 jul 2024
Last Updated: 15 jul 2024

Year: 2024

Abstract:

We consider an optimization problem related to elliptic PDEs of the form $-{\rm div}(a(x)\nabla u)=f$ with Dirichlet boundary condition on a given domain $\Omega$. The coefficient $a(x)$ has to be determined, in a suitable given class of admissible choices, in order to optimize a given criterion. We first deal with the case when the cost is the so-called elastic compliance, and then we discuss the more general case when the problem is written as an optimal control problem.

Keywords: regularity, shape optimization, optimal control problems, optimal coefficients


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