2023-11-30T12:21:04Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/445012023-08-25T13:15:26Zcom_20.500.14352_14col_20.500.14352_15
On the optimal control for a semilinear equation with cost depending on the free boundary
Díaz Díaz, Jesús Ildefonso
Mingazzini, Tomasso
Ramos del Olmo, Ángel Manuel
We study an optimal control problem for a semilinear elliptic boundary value problem giving rise to a free boundary. Here, the free boundary is generated due to the fact that the nonlinear term of the state equation is not differentiable. The new aspect considered in this paper, with respect to other control problems involving free boundaries, is that here the cost functional explicitly depends on the location of the free boundary. The main difficulty is to show the continuous dependence (in measure) of the free boundary with respect to the control function. The crucial tool to get such continuous dependence is to know how behaves the state solution near the free boundary, as in previous works by L.A. Caffarelli and D. Phillips among other authors. Here we improved previous results in the literature thanks to a suitable application of the Fleming-Rishel formula.
2023-06-20T03:49:17Z
2023-06-20T03:49:17Z
2023-06-20T03:49:17Z
2012
journal article
https://hdl.handle.net/20.500.14352/44501
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1556-1801
10.3934/nhm.2012.7.605
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American Institute of Mathematical Sciences