O 19. a 20. Hilbertově problému
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
We consider a model for the control of a linear network flow system with unknown but bounded demand and polytopic bounds on controlled flows. We are interested in the problem of finding a suitable objective function that makes robust optimal the policy represented by the so-called linear saturated feedback control. We regard the problem as a suitable differential game with switching cost and study it in the framework of the viscosity solutions theory for Bellman and Isaacs equations.
Sia quasiconvessa in , quasiperiodica in nel senso di Besicovitch e soddisfi le disuguaglianze: Allora può essere omogeneizzata: esiste una funzione che dipende solo da tale che i funzionali convergono, per tendente a (nel senso della -convergenza) a Inoltre si può dare una formula asintotica per .
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
A Bernoulli free boundary problem with geometrical constraints is studied. The domain Ω is constrained to lie in the half space determined by x1 ≥ 0 and its boundary to contain a segment of the hyperplane {x1 = 0} where non-homogeneous Dirichlet conditions are imposed. We are then looking for the solution of a partial differential equation satisfying a Dirichlet and a Neumann boundary condition simultaneously on the free boundary. The existence and uniqueness of a solution have already been addressed...
2000 Mathematics Subject Classification: 35J40, 49J52, 49J40, 46E30By means of a suitable nonsmooth critical point theory for lower semicontinuous functionals we prove the existence of infinitely many solutions for a class of quasilinear Dirichlet problems with symmetric non-linearities having a one-sided growth condition of exponential type.The research of the authors was partially supported by the MIUR project “Variational and topological methods in the study of nonlinear phenomena” (COFIN 2001)....
We present here our most recent results ([1def]) about the definition of non-linear Weiertrass-type integrals over BV varieties, possibly discontinuous and not necessarily Sobolev's.