Viscosity Solutions and Applications: Lectures Given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) Held in Montecatini Terme, Italy, June, 12 - 20, 1995The volume comprises five extended surveys on the recent theory of viscosity solutions of fully nonlinear partial differential equations, and some of its most relevant applications to optimal control theory for deterministic and stochastic systems, front propagation, geometric motions and mathematical finance. The volume forms a state-of-the-art reference on the subject of viscosity solutions, and the authors are among the most prominent specialists. Potential readers are researchers in nonlinear PDE's, systems theory, stochastic processes. |
Contents
The uniqueness machinery for second order equations | 28 |
Proof of the theorem on sums | 34 |
0 | 40 |
Copyright | |
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applications approximation assume assumptions asymptotic Barles boundary condition bounded classical compact control problems convergence convex D²u defined definition differential games Dip.to di Matematica Dirichlet problem discontinuous discounted minimum Dynamic Programming Dynamic Programming Principle estimates evolution example exists finite fully nonlinear geometric Hamilton-Jacobi equations Hamilton-Jacobi-Bellman equations horizon problem inequality infinite horizon problem Ishii Lecture Lemma level set linear Lipschitz continuous Math Mathematics maximum principle mean curvature minimum time problem motion normal velocity optimal control optimal feedback P.L. Lions partial differential equations player proof of Theorem properties Proposition prove refer resp result satisfies second order Section set evolution smooth Soner Soravia Souganidis stochastic supersolution Theorem 3.2 theory of viscosity uniformly unique upper semicontinuous value function value problem Verification Theorem viscosity solutions weak limit