Publications


[60]  “Functions which are quasiconvex under linear perturbations,” (with E. Barron and R. Goebel) SIAM Journal on Optimization, to appear.

[59]  “The quasiconvex envelope through 1rst-order partial differential equations which characterize quasiconvexity of nonsmooth functions,” (with E. Barron and R. Goebel) Dynamical Control Systems, Volume 17, Issue 6, 2012, 1693 - 1706.

[58]  “Quasiconvex functions and Nonlinear PDEs" (with E. Barron and R. Goebel) Transactions of the American Mathematical Society, to appear.

[57]  “Best response dynamics for continuous games,” (with E. Barron and R. Goebel) Proceedings of the American Mathematical Society, 138 (2010), no.3 1069—1083.

[56]  “Uniqueness and nonuniqueness of viscosity solutions to Aronsson's equation," (with C. Wang and Y. Yu) Archive for Rational Mechanics and Analysis 190 (2008), no. 2, 347--370.

[55]  “The infinity Laplacian, Aronsson's equation, and their generalizations," (with E. N. Barron and L. C. Evans) Transactions of the American Mathematical Society 360 (2008), no. 1, 77—101.

[54]  “Minimizing the L∞ norm of the gradient with an energy constraint ," (with E. N. Barron) Communications in Partial Differential Equations 30 (2005), 1741-1772.

[53]  “Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE," (with A. Swiech) Communications on Pure and Applied Analysis 4 (2005) no. 1, 199-207.

[52]  “Conditional essential suprema with applications ," (with E. N. Barron) Applied Mathematics and Optimization 48 (2003), no. 3, 229-253.

[51]  “A geometric characterization of viable sets for controlled degenerate diffusions," (with M. Bardi) Set-Valued Analysis 10 (2002), no. 2-3, 129-141.

[50]  “Good and viscosity solutions of fully nonlinear elliptic equations," (with M. Kocan, and A. Swiech) Proceedings of the American Mathematical Society 130 (2002), 533-542.

[49]  “Euler Equation and Absolute minimizers of L∞ functionals," (with E. N. Barron and C. Y. Wang) Archive for Rational Mechanics and Analysis 157 (2001), 255-283.

[48]  “Lower semicontinuity of L∞ functionals," (with E. N. Barron and C. Wang) Annales Institut Henri Poincare, Nonlineaire Analyse, 4 (2001), 495-517.

[47]  “Lyapunov Stability using minimum distance control," (with E. N. Barron) Nonlinear Anaysis 43 (2001), no. 7, Ser. A: Theory Methods, 923-936.

[46]  “Radon-Nikodym theorem in L∞," (with E. N. Barron and P. Cardaliaguet) Applied Mathematics and Optimization 42 (2000), no. 2, 103-126.

[45]  “Barron,  Regularity of Hamilton-Jacobi equations when forward is backward," (with E. N. Barron, P. Cannarsa, and C. Sinestrari) Indiana University Mathematics Journal 48 (1999), no. 2, 385-409.

[44]  “Applications of the Hopf-Lax formula for ut + H(u;Du) = 0," (with E. N. Barron and W. Liu) SIAM Journal on Mathematical Analysis 29 (1998), no. 4, 1022-1039.

[43]  “The L∞  control problem with continuous control functions," (with E. Barron and W. Liu) Nonlinear Analysis 32 (1998), no. 1, 1-14.

[42]  “Hopf-Lax type formula for ut + H(u;Du) = 0. II." (with E. N. Barron and W. Liu) Communications in Partial Differential Equations 22 (1997), no. 7-8, 1141-1160.

[41]  “Explicit solution of some first-order PDE's," (with E. N. Barron and W. Liu) Journal of Dynamical and Control Systems 3 (1997), no. 2, 149-164.

[40]  “A Hopf-Lax type formula for ut + H(u;Du) = 0," (with E. Barron and W. Liu) Journal of Differential Equations 126 (1996), no. 1, 48-61.

[39]  “Relaxation of constrained optimal control problems," (with E. Barron), SIAM Journal on Control and Optimization 34 (1996), no. 6, 2077-2091.

[38]  “Uniformly elliptic pdes with bounded, measurable coefficients," Journal of Fourier Analysis and Applications, 2(1996), 237-259.

[37]  “Optimal control of the blow-up time of a diffusion," (with E. Barron and W. Liu), Mathematical Models and Methods in Applied Sciences 6 (1996), no. 5, 665-687.

[36]  “Relaxed minimax control" (with E. Barron), SIAM Journal of Control and Optimization 33(1995), 1028-1039.

[35] “Uniqueness of Lipschitz extensions: Minimizing the sup-norm of the gradient," Archive for Rational Mechanics and Analysis, 123(1993), 51-74.

[34]  “Optimal control and differential games with measures," (with E. Barron and J. L. Menaldi), Journal of Nonlinear Analysis, 21(1993), 241-268.

[33]  “Optimal control and semicontinuous viscosity solutions," (with E. Barron), Proceedings of the American Mathematical Society, 113(1991), 397-402.

[32]  “Total risk aversion and the pricing of options," (with E. Barron), Applied Mathematics and Optimization, 23(1991), 51-76.

[31]  “Semicontinuous viscosity solutions for Hamilton-Jacobi equations with convex Hamiltonians," (with E. Barron), Communications in Partial Differential Equations, 15(1990), 1713-1742.

[30]  “A stochastic control approach to the pricing of options," (with E. Barron), Mathematics of Operations Research, 15(1990), 49-79.

[29]  “Uniqueness criteria for viscosity solutions of fully nonlinear elliptic partial differential equations," Indiana University Mathematics Journal, 38(1989), 629-667.

[28]  “Total risk aversion, stochastic optimal control, and differential games," (with E. Barron), Applied Mathematics and Optimization, 19(1989), 313-327.

[27]  “A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations," (with P.-L. Lions and P. E. Souganidis), Proceedings of the American Mathematical Society, 4(1988), 975-978.

[26]  “Viscosity solutions for fully nonlinear second order equations with applications to stochastic differential games," Proceedings of the 25th IEEE Conference on Decision and Control, Athens, Greece December 1986.

[25]  “The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations," Archive for Rational Mechanics and Analysis, 1(1988), 1-27.

[24]  “The necessary conditions for optimal control in Hilbert spaces," (with V. Barbu and E. Barron), Journal of Mathematical Analysis and Applications, 133(1988), 151-162.

[23]  “Generalized viscosity solutions for Hamilton-Jacobi equations with time measurable Hamiltonians," (with E. Barron), Journal of Differential Equations, 1(1987), 10-21.

[22]  “A regularity result for viscosity solutions of Hamilton-Jacobi equations in one space variable," (with P. E. Souganidis), Transactions of the American Mathematical Society, 301(1987), 137-147.

[21]  “Minimizing a quadratic payoff with monotone controls," (with E. Barron and A. G. Malliaris), Mathematics of Operations Research, 2(1987), 297-308.

[20]  “The Pontryagin maximum principle from dynamic programming and viscosity solutions to first order partial differential equations," (with E. Barron), Transactions of the American Mathematical Society, 2(1986), 635-641.

[19]  “On the Kleinrock, Nilsson problem of optimal scheduling algorithms for time shared systems," (with E. Barron), Journal of Optimization Theory and Applications, 50(1986), 49-60.

[18]  “Viscosity solutions of Isaacs' equations and differential games with Lipschitz controls," (with E. Barron and L. C. Evans), Journal of Differential Equations, 53(1984), 213-233.

[17]  “The Berkowitz example in monotone games," (with E. Barron), Journal of Mathematical Analysis and Applications, (addendum to [15]).

[16]  “A nonlinear evolution system with two subdifferentials and monotone differential games," (with E. Barron), Journal of Mathematical Analysis and Applications,97(1983), 65-80.

[15]  “Some asymptotic problems in fully nonlinear elliptic equations and stochastic control," (with P.-L. Lions), Annali Della Scuola Normale Superiore di Pisa, 4(1984), 129-176.

[14]  “Regularity for elasto-plastic type variational inequalities," Indiana University Mathematics Journal, 3(1983), 407-423.

 [13]  “A boundary gradient estimate for harmonic functions and applications,” (with L. C. Evans) Nonlinear partial differential equations and their applications. Collège de France Seminar, Vol. I (Paris, 1978/1979), pp. 160–176, Res. Notes in Math., 53, Pitman, Boston, Mass.-London, 1981.

[12]  “Boundary regularity for variational inequalities," Indiana University Mathematics Journal, 4(1980), 495-504.

[11]  “Optimal control with no turning back," (with E. Barron), Journal of Differential Equations, 2(1980), 223-248.

 [10]  “Monotonicity is necessary and sufficient for compensated compactness," Mathematics Research Center, University of Wisconsin Technical Report  #1845.

 [9]  “Fluid flow through a porous media," Free Boundary Problems, proceedings of a seminar held in Pavia, Italy September-October 1979.

[8]  “A nonsteady flow of liquid in a porous pipe with variable permeability," (with A. Friedman), Journal of Differential Equations, 1(1979), 1-24.

 [7]  “Uniqueness of solutions to -Δu - qu=0," Communications in Partial Differential Equations, 3(1978), 1053-1076.

[6]  “Smoothness of the free boundary in the Stefan problem with supercooled water," Illinois Journal of Mathematics, 4(1978), 623-269.

[5]  “Structure of the nonmonotone free boundaries in a Filtration problem," Indiana University Mathematics Journal, 6(1977), 1121-1135.

[4] “Convexity of the free boundary in the Stefan problem and in the dam problem," (with A. Friedman) Archive for Rational Mechanics and Analysis, 1(1977), 1-24.

[3]  “Elliptic quasi-variational inequalities and applications to a non-stationary problem in hydraulics," (with A. Friedman), Annali Della Scuola Normale Superiore di Pisa, 1(1976), 47-88.

[2]  “A parabolic quasi-variational inequality arising in hydraulics," (with A. Friedman), Annali Della Scuola Normale Superiore di Pisa, 3(1975), 421-468.

[1]  “Finite difference approximation to the free boundary of a parabolic variational inequality," Ph. D. thesis.