Abstract

We consider an optimization problem related to elliptic PDEs of the form −div(a(x)∇u)=f-\text{div}(a(x)\nabla u)=f with Dirichlet boundary condition on a given domain Ω\Omega. The coefficient a(x)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.

Author information

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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

Keywords

  • Shape optimization
  • optimal coefficients
  • regularity
  • optimal control problems

Mathematics Subject Classification

49Q10, 49J45, 35B65, 35R05, 49K20

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Suggested citation

G. Buttazzo, J. Casado-Díaz, F. Maestre. “Optimal Coefficients for Elliptic PDEs.” Journal of Convex Analysis 33 (2026), No. 3&4, 765–780. https://doi.org/10.68381/jca33043

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press.