{"ID":2831121,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.08431","arxiv_id":"2512.08431","title":"Optimal coefficients for elliptic PDEs","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 $Ω$. 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.","short_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 $Ω$. 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...","url_abs":"https://arxiv.org/abs/2512.08431","url_pdf":"https://arxiv.org/pdf/2512.08431v1","authors":"[\"Giuseppe Buttazzo\",\"Juan Casado-Díaz\",\"Faustino Maestre\"]","published":"2025-12-09T09:58:55Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}