Singularities of polar curves
Infinitely near imposed singularities and singularities of polar curves.
Filtrations by Complete Ideals and Applications
Filtrations by complete ideals and applications.
An algorithm for indefinite quadratic programming based on a partial Cholesky factorization
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
Optimal control of an ill-posed elliptic semilinear equation with an exponential non linearity
We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity, such that we cannot expect to have a solution of the state equation for any given control. We then have to speak of pairs (control, state). After having defined a suitable functional class in which we look for solutions, we prove existence of an optimal pair for a large class of cost functions using a non standard compactness argument. Then, we derive a first order optimality system assuming...
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