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arXiv · 2512.08431

Optimal coefficients for elliptic PDEs

Giuseppe Buttazzo·Juan Casado-Díaz·Faustino Maestre
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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.

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Giuseppe Buttazzo, Juan Casado-Díaz, Faustino Maestre. 2025-12-09. Optimal coefficients for elliptic PDEs. https://arxiv.org/abs/2512.08431

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