Journal of Convex Analysis 33 (2026), No. 3&4, 765--780
Copyright Heldermann Verlag 2026
Optimal Coefficients for Elliptic PDEs
Giuseppe Buttazzo
Dipartimento di Matematica, Università di Pisa, Italy, Italy
giuseppe.buttazzo@unipi.it
Juan Casado-Díaz
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Sevilla, Spain
jcasadod@us.es
Faustino Maestre
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Sevilla, Spain
fmaestre@us.es
[Abstract-pdf]
We consider an optimization problem related to elliptic PDEs of the form $-\text{div}(a(x)\nabla u)=f$ 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: Shape optimization, optimal coefficients, regularity, optimal control problems.
MSC: 49Q10, 49J45, 35B65, 35R05, 49K20.
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