Souganidis, P. E.
Overview
Works:  14 works in 25 publications in 1 language and 21 library holdings 

Publication Timeline
.
Most widely held works by
P. E Souganidis
Viscosity solutions of secondorder 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
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 HamiltonJacobiIsaacs 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 twoperson, zerosum differential games and the new notion of viscosity solutions of HamiltonJacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a twoperson, zerosum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following ElliottKalton. 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 firstorder PDE. This is then used to prove results about the level sets of solutions of HamiltonJacobi equations with homogeneous Hamiltonians. These results are also related to the theory of Huygen's principle and geometric optics
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 twoperson, zerosum differential games and the new notion of viscosity solutions of HamiltonJacobi PDE, (Partial Differential Equations). The basic idea is that the dynamic programming optimality conditions imply that the values of a twoperson, zerosum differential game are viscosity solutions of appropriate PDE. This paper proves the above, when the values of the differential games are defined following ElliottKalton. 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 firstorder PDE. This is then used to prove results about the level sets of solutions of HamiltonJacobi 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 twoperson, zerosum differential games problems and the new notion of viscosity solutions of HamiltonJacobi 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 HamiltonJacobiBellman 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)
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 twoperson, zerosum differential games problems and the new notion of viscosity solutions of HamiltonJacobi 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 HamiltonJacobiBellman 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
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
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
1 edition published in 1998 in English and held by 1 WorldCat member library worldwide
A regularity result for viscosity solutions of HamiltonJacobi 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
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
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
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
1 edition published in 1985 in English and held by 1 WorldCat member library worldwide
PDEviscosity 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
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
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
1 edition published in 1986 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Lions, PierreLouis Author
 Evans, L. C. Author
 Fleming, W. H. Author
 University of Minnesota Institute for Mathematics and Its Applications
 WISCONSIN UNIVMADISON MATHEMATICS RESEARCH CENTER
 Brown University Center for Control Sciences
 Barles, G. Author
 Lefschetz Center for Dynamical Systems
 MAZZEO, R.
 Perthame, B. Author
Languages