On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
Guy Barles, Francesca Da Lio (2005)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “On ergodic problem for Hamilton-Jacobi-Isaacs equations”
On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions
A general Hamilton-Jacobi framework for non-linear state-constrained control problems
Albert Altarovici, Olivier Bokanowski, Hasnaa Zidani (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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The paper deals with deterministic optimal control problems with state constraints and non-linear dynamics. It is known for such problems that the value function is in general discontinuous and its characterization by means of a Hamilton-Jacobi equation requires some controllability assumptions involving the dynamics and the set of state constraints. Here, we first adopt the viability point of view and look at the value function as its epigraph. Then, we prove that this epigraph can...
Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls
Hong Qiu, Jiongmin Yong (2013)
ESAIM: Control, Optimisation and Calculus of Variations
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A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs’ condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of...
PDE-viscosity solution approach to some problems of large deviations
Wendell H. Fleming, Panagiotis E. Souganidis (1986)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Viscosity solutions of the Isaacs equation οn an attainable set
Leszek Zaremba (1994)
Applicationes Mathematicae
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We apply a modification of the viscosity solution concept introduced in [8] to the Isaacs equation defined on the set attainable from a given set of initial conditions. We extend the notion of a lower strategy introduced by us in [17] to a more general setting to prove that the lower and upper values of a differential game are subsolutions (resp. supersolutions) in our sense to the upper (resp. lower) Isaacs equation of the differential game. Our basic restriction is that the variable...
Ergodic problem for the Hamilton-Jacobi-Bellman equation. II
Mariko Arisawa (1998)
Annales de l'I.H.P. Analyse non linéaire
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Comparison and existence results for evolutive non-coercive first-order Hamilton-Jacobi equations
Alessandra Cutrì, Francesca Da Lio (2007)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper we prove a comparison result between semicontinuous viscosity subsolutions and supersolutions to Hamilton-Jacobi equations of the form in where the Hamiltonian may be noncoercive in the gradient As a consequence of the comparison result and the Perron's method we get the existence of a continuous solution of this equation.
Hamilton-Jacobi equations for control problems of parabolic equations
Sophie Gombao, Jean-Pierre Raymond (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power – where is an unbounded operator in a Hilbert space – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already...