Optimal coefficients for elliptic PDEs

2025/12/09 by Buttazzo, Giuseppe, Casado-Díaz, Juan, Maestre, Faustino
Computer Science · Mathematics · #35B65 #35R05 #49J45 #49K20 #49Q10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.2512.08431

openalex publication_date 2025/12/09 · openalex created_date 2025/12/11 · openalex updated_date 2026/07/28

Abstract

We consider an optimization problem related to elliptic PDEs of the form -\rm div(a(x)∇ u)=f with Dirichlet boundary condition on a given domain Ω. 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.

Citations

• On the regularity of optimal potentials in control problems governed by elliptic equations
• Mass optimization problem with convex cost
• An Unstable Elliptic Free Boundary Problem arising in Solid Combustion
• Exact estimates of the conductivity of a binary mixture of isotropic materials

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