Educational Background

Ph.D. University of Minnesota 1997

Selected Publications

J. Kovats. On the Second Order Derivatives of Solutions of a Special Isaacs Equations. Proceedings of the AMS, 2016 (144)  pp. 1523-1533

J. Kovats. The Minmax Principle and W^{2,p} Regularity for Solutions of the Simplest Isaacs Equations. Proceedings of the AMS, 2012 (140)  pp. 2803-2815

J. Kovats. Value Functions and the Dirichlet Problem for Isaacs Equation in a Smooth Domain.Transactions of the AMS, 2009 (361) pp. 4045-4076

J. Kovats. Stopped Markov Processes and Applications to the Dirichlet Problem in a Smooth Domain. Markov Processes and Related Fields . December 2009

J. Kovats. Differentiability Properties of Solutions of Nondegenerate Isaacs Equations, Proceedings of the World Congress of Nonlinear Analysts 2008, Nonlinear Analysis: Theory Methods and Applications, May 2009

J. Kovats. On the Regularity of Viscosity Solutions of Fully Nonlinear Elliptic Equations, Proceedings of the World Congress of Nonlinear Analysts, Nonlinear Analysis, 2005, Vol. 63, pp. 1341-1350

J. Kovats. A 3-Curves Theorem for Viscosity Subsolutions of Parabolic Equations, Proceedings of the AMS, 2003, Vol. 131 (5), pp. 1509-1514

J. Kovats. Fully Nonlinear Elliptic Equations and the Dini Condition, Communications in PDE, 1997, Vol. 22 (11-12), pp. 1911-1927.

Research

I am currently interested in the regularity of solutions of fully nonlinear elliptic partial differential equations. The prototypical example of such a pde is the Isaacs equation, which has its origins in the theory of stochastic differential games. A major area of pde research focuses on questions about the smoothness of solutions to these equations. Even in the simplest, constant coefficient case (and with no lower order terms), little is known about the continuity and integrability properties of the second order derivatives of solutions.

Research & Project Interests

Viscosity Solutions of Fully Nonlinear Elliptic Equations

The Singular Set for Solutions of Isaacs Equations