Papers by Andrzej Swiech

  1. Sub- and superoptimality principles and construction of almost optimal strategies for differential games in Hilbert spaces, A. Swiech, to appear in Annals of the ISDG, vol. XI.
  2. Existence of strong solutions of Pucci extremal equations with superlinear growth in $Du$, S. Koike and A. Swiech, J. Fixed Point Theory Appl. 5 (2009), no. 2, 291--304.
  3. Weak Harnack inequality for fully nonlinear uniformly elliptic PDE with unbounded ingredients, S. Koike and A. Swiech, J. Math. Soc. Japan. 61 (2009), no. 3, 723--755.
  4. A PDE approach to large deviations in Hilbert spaces, A. Swiech, Stochastic Process. Appl. 119 (2009), no. 4, 1081--1123.
  5. Verification theorem and construction of $\epsilon$-optimal controls for control of abstract evolution equations, G. Fabbri, F. Gozzi and A. Swiech, to appear in J. Convex Anal..
  6. Regularity for obstacle problems in infinite dimensional Hilbert spaces, A. Swiech and E. V. Teixeira, Adv. Math. 220 (2009), no. 3, 964--983.
  7. Maximum principle for fully nonlinear equations via the iterated comparison function method, S. Koike and A. Swiech, Math. Ann. 339 (2007), no. 2, 461--484.
  8. Perron's method and the method of relaxed limits for ``unbounded" PDE in Hilbert spaces, D. Kelome and A. Swiech, Studia Math. 176 (2006), no. 3, 249--277.
  9. Bellman equations associated to the optimal feedback control of stochastic Navier-Stokes equations, F. Gozzi, S. S. Sritharan and A. Swiech, Communications on Pure and Applied Mathematics 58 (2005), 671-700.
  10. Uniqueness and existence of maximal and minimal solutions of fully nonlinear elliptic PDE, R. Jensen and A. Swiech, Communications on Pure and Applied Analysis 4 (2005), no. 1, 187-195.
  11. A corrected proof of the stochastic verification theorem within the framework of viscosity solutions, F. Gozzi, A. Swiech and X. Y. Zhou, SIAM J. Control Optim. 43 (2005), no. 6, 2009--2019.
  12. Maximum principle and existence of $L^p$-viscosity solutions for fully nonlinear uniformly elliptic equations with measurable and quadratic terms, S. Koike and A. Swiech, NoDEA Nonlinear Differential Equations Appl. 11 (2004), no. 4, 491-509.
  13. A note on generalized maximum principles for elliptic and parabolic PDE, M. G. Crandall and A. Swiech, in Evolution Equations, Proceedings in honor of J. A. Goldstein's 60th birthday (Goldstein, Nagel and Romanelli eds.), Lecture notes in pure and applied mathematics, vol. 235, Marcel Dekker, 2003, 121--127.
  14. Viscosity solutions of an infinite-dimensional Black-Scholes-Barenblatt equation, D. Kelome and A. Swiech, Appl. Math. Optim. 47 (2003), no. 3, 253--278.
  15. Viscosity solutions of dynamic programming equations for the optimal control of Navier-Stokes equations, F. Gozzi, S.S. Sritharan, and A. Swiech, Arch. Ration. Mech. Anal. 163 (2002), no. 4, 295--327.
  16. Risk-sensitive control and differential games in infinite dimensions, A. Swiech, Nonlinear Anal. 50 (2002), no. 4, Ser. A: Theory Methods, 509--522.
  17. Good and viscosity solutions of fully nonlinear elliptic equations, R. Jensen, M. Kocan, and A. Swiech, Proceedings of the American Mathematical Society 130 (2002), no. 2, 533-542.
  18. Hamilton-Jacobi-Bellman equations for the optimal control of the Duncan-Mortensen-Zakai equation, F. Gozzi, and A. Swiech, Journal of Functional Analysis 172 (2000), no. 2, 466-510.
  19. $L^p$-Theory for fully nonlinear uniformly parabolic equations, M.G. Crandall, M. Kocan, and A. Swiech, Communications in Partial Differential Equations 25 (2000), no. 11&12, 1997--2053.
  20. Existence results for boundary problems for uniformly elliptic and parabolic fully nonlinear equations, M.G. Crandall, M. Kocan, P.L. Lions, and A. Swiech, Electronic Journal of Differential Equations, Vol. 1999 (1999), No. 24, 1--20.
  21. Remarks on nonlinear, uniformly parabolic equations, M.G. Crandall, P. Fok, M. Kocan, and A. Swiech, Indiana University Mathematics Journal 47 (1998), no. 4, 1293--1326.
  22. Second order Hamilton-Jacobi equations in Hilbert spaces and stochastic boundary control, F. Gozzi, E. Rouy, and A. Swiech, SIAM J. Control Optim. 38 (2000), no. 2, 400-430.
  23. Incentive compatibility constraints and dynamic programming in continuous time, E. Barucci, F. Gozzi, and A. Swiech, Journal of Mathematical Economics 34 (2000), no. 4, 471--508.
  24. Optimal stopping in Hilbert spaces and pricing of American options, D. Gatarek, and A. Swiech, Mathematical Methods of Operations Research 50 (1999), 135--147.
  25. $W^{1,p}$-Interior estimates for solutions of fully nonlinear, uniformly elliptic equations, A. Swiech, Advances in Differential Equations 2 (1997), no. 6, 1005--1027.
  26. Optimal maps for the Multidimensional Monge-Kantorovich Problem, W. Gangbo, and A. Swiech, Communications on Pure and Applied Mathematics 51 (1998), no. 1, 23--45.
  27. On differential games for infinite dimensional systems with nonlinear, unbounded operators, M. Kocan, P. Soravia, and A. Swiech, Journal of Mathematical Analysis and Applications 211 (1997), 395--423.
  28. A note on the differences of the consecutive powers of operators, A. Swiech, Linear Operators, J. Janas, F. H. Szafraniec, and J. Zemanek (eds.), Banach Center Publ. vol. 38, Institute of Mathematics, Polish Academy of Sciences, Warsaw, 1997, 381--383.
  29. Another approach to the existence of value functions of stochastic differential games, A. Swiech, Journal of Mathematical Analysis and Applications 204 (1996), no. 3, 884--897.
  30. Least squares integration of one-dimensional codistributions with application to approximate feedback linearization, A. Banaszuk, J. Hauser, and A. Swiech, Mathematics of Controls, Signals and Systems 9 (1996), no. 3, 207--241.
  31. Perturbed optimization on product spaces, M. Kocan and A. Swiech, Nonlinear Anal. 26 (1996), no. 1, 81--90.
  32. On the equivalence of various weak notions of solutions of elliptic PDE's with measurable ingredients, M.G. Crandall, M. Kocan, P. Soravia, and A. Swiech, Progress in Elliptic and Parabolic PDE's (A. Alvino et al. eds.), Pitman Research Notes in Math., vol. 350, 1996, 136--162.
  33. Sub- and superoptimality principles of dynamic programming revisited, A. Swiech, Nonlinear Analysis, Theory, Methods and Applications 26 (1996), 1429--1436.
  34. On viscosity solutions of fully nonlinear equations with measurable ingredients, L. Caffarelli, M.G. Crandall, M. Kocan, and A. Swiech, Communications on Pure and Applied Mathematics 49 (1996), 365--397.
  35. Second order unbounded parabolic equations in separated form, M. Kocan, and A. Swiech, Studia Mathematica 115 (1995), 291--310.
  36. Unbounded second order partial differential equations in infinite dimensional Hilbert spaces, A. Swiech, Communications in Partial Differential Equations 19 (11&12) (1994), 1999-2036.
  37. On partial sup-convolutions, a lemma of P.L. Lions and viscosity solutions in Hilbert spaces, M.G. Crandall, M. Kocan, and A. Swiech, Advances in Mathematical Sciences and Applications 3 (1993/4), 1--15.
  38. Spectral characterization of operators with precompact orbit, A. Swiech, Studia Math. 96 (1990), no. 3, 277--282.

Papers 1-8 have been supported by the NSF grant DMS 0500270.