WorldCat Identities

Souganidis, P. E.

Overview
Works: 14 works in 25 publications in 1 language and 21 library holdings
Publication Timeline
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Most widely held works by P. E Souganidis
Viscosity solutions of second-order equations, control and stochastic differential games by P. L Lions( Book )

3 editions published between 1986 and 1987 in English and held by 3 WorldCat member libraries worldwide

Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations by United States( Book )

3 editions published in 1983 in English and held by 3 WorldCat member libraries worldwide

Recent work by the authors and others has demonstrated the connections between the dynamic programming approach for two-person, zero-sum differential games and the new notion of viscosity solutions of Hamilton-Jacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a two-person, zero-sum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following Elliott-Kalton. This results in a great simplification in the statements and proofs, as the definitions are explicit and do not entail any kind of approximations. Moreover, as an application of the above results, the paper contains a representation formula for the solution of a fully nonlinear first-order PDE. This is then used to prove results about the level sets of solutions of Hamilton-Jacobi equations with homogeneous Hamiltonians. These results are also related to the theory of Huygen's principle and geometric optics
Differential Games, Optimal Control and Directional Derivatives of Viscosity Solutions of Bellman's and Isaacs' Equations by United States( Book )

2 editions published in 1984 in English and held by 2 WorldCat member libraries worldwide

Recent work by the authors and others has demonstrated the connections between the dynamic programming approach to optimal control theory and to two-person, zero-sum differential games problems and the new notion of viscosity solutions of Hamilton-Jacobi PDE's introduced by M.G. Crandall and P.L. Lions. In particular, it has been proved that the dynamic programming principle implies that the value function is the viscosity solution of the associated Hamilton-Jacobi-Bellman and Isaacs equations. In the present work, it is shown that viscosity super- and subsolutions of these equations must satisfy some inequalities called super- and subdynamic programming principle respectively. This is then used to prove the equivalence between the notion of viscosity solutions and the conditions, introduced by A. Subbotin, concerning the sign of certain generalized directional derivatives. (Author)
Convergence of approximation schemes for fully nonlinear second order equations by Guy Barles( Book )

2 editions published in 1990 in English and held by 2 WorldCat member libraries worldwide

A stochastic control approach to some large deviations problems by Wendell H Fleming( Book )

1 edition published in 1984 in English and held by 1 WorldCat member library worldwide

A limiting case for velocity averaging by B Perthame( Book )

1 edition published in 1998 in English and held by 1 WorldCat member library worldwide

A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space dimension by University of Minnesota( Book )

1 edition published in 1986 in English and held by 1 WorldCat member library worldwide

A PDE approach to geometric optics for certain semilinear parabolic equations by L. C Evans( Book )

2 editions published in 1987 in English and held by 1 WorldCat member library worldwide

Differential games and directional derivatives of viscosity solutions of Isaacs' equations II by University of Minnesota( Book )

1 edition published in 1985 in English and held by 1 WorldCat member library worldwide

Asymptotic series and the method of vanishing viscosity by University of Minnesota( Book )

1 edition published in 1985 in English and held by 1 WorldCat member library worldwide

PDE-viscosity solution approach to some problems of large deviations by Wendell H Fleming( Book )

1 edition published in 1984 in English and held by 1 WorldCat member library worldwide

A PDE approach to asymptotic estimates for optimal exit probabilities by Wendell H Fleming( Book )

1 edition published in 1984 in English and held by 1 WorldCat member library worldwide

The relation between the porous medium and the eikonal equations in several space dimensions by P. L Lions( Book )

1 edition published in 1986 in English and held by 1 WorldCat member library worldwide

 
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Audience Level
0
Audience Level
1
  Kids General Special  
Audience level: 0.83 (from 0.76 for Viscosity ... to 0.88 for A limiting ...)

Languages
English (20)