RT Journal Article
T1 On the optimal control for a semilinear equation with cost depending on the free boundary
A1 Díaz Díaz, Jesús Ildefonso
A1 Mingazzini, Tomasso
A1 Ramos Del Olmo, Ángel Manuel
AB 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.
PB American Institute of Mathematical Sciences
SN 1556-1801
YR 2012
FD 2012
LK https://hdl.handle.net/20.500.14352/44501
UL https://hdl.handle.net/20.500.14352/44501
LA eng
NO Unión Europea. FP7
NO Comunidad de Madrid
NO UCM
NO DGISPI, Spain
NO AMR
NO Fundación Caja Madrid
DS Docta Complutense
RD 14 jun 2025