Selected preprints and publications of Mikhail Feldman.

This material is based upon work supported by the National Science Foundation under various grants.

`` The semi-geostrophic system: weak-strong uniqueness under uniform convexity" (with A. Tudorascu), Calc. Var. Partial Differential Equations 56 (2017), no. 6, 56:158.

``Semi-geostrophic System with Variable Coriolis parameter'' (with J. Cheng and M. Cullen), Arch. Ration. Mech. Anal. 227 (2018), no. 1, 215--272.

``Transonic Flows with Shocks Past Curved Wedges for the Full Euler Equations'' (with G.-Q. Chen and J. Chen), Discrete Contin. Dyn. Syst. 36 (2016), no. 8, 4179-4211.

"Lagrangian solutions for the Semi-Geostrophic Shallow Water system in physical space with general initial data" (with A. Tudorascu), St. Petersburg Mathematical Journal, Volume 27, Issue 3, 2016, 547-568

"On the semi-geostrophic system in physical space with general initial data" (with A. Tudorascu), Arch. Ration. Mech. Anal. 218 (2015), no. 1, 527-551.

``Prandtl-Meyer reflection for supersonic flow past a solid ramp'' (with M. Bae and G.-Q. Chen), Quart. Appl. Math. 71 (2013), 583-600

``On Lagrangian solutions for the semi-geostrophic system with singular initial data'' (with A. Tudorascu), SIAM J. Math. Anal. 45 (2013), no. 3, 1616-1640.

``Comparison principles for self-similar potential flow'' (with G.-Q. Chen), Proc. Amer. Math. Soc. 140 (2012), no. 2, 651-663

"Transonic Shocks In Multidimensional Divergent Nozzles" (with M. Bae), Arch. Ration. Mech. Anal. 201 (2011), no. 3, 777-840

``Regularity of Solutions to Regular Shock Reflection for Potential Flow" (with M. Bae and G.-Q. Chen), Invent. Math. 175(2009) no 3, pp. 505-543

``Global Solutions to Shock Reflection by Large-Angle Wedges for Potential Flow'' (with G.-Q. Chen), Annals of Math. 171 (2010), No. 2, pp. 1067-1182

``Transonic Shocks and Free Boundary Problems for the Full Euler Equations in Infinite Nozzles'' (with G.-Q. Chen and J. Chen), J. Math. Pures Appl. 88(2007), no.2, pp. 191--218.

``Existence and Stability of Multidimensional Transonic Flows through an Infinite Nozzle of Arbitrary Cross-Sections'' (with G.-Q. Chen), Arch. Ration. Mech. Anal 184(2007), no 2, pp. 185-242.

"Self-similar isothermal irrotational motion for the Euler, Euler-Poisson systems and the formation of the plasma sheath.", (with S.-Y. Ha and M. Slemrod).
J. Hyperbolic Differ. Equ. 3 (2006), no. 2, pp. 233--246.

``Lagrangian solutions of semigeostrophic equations in physical space'' (with M. Cullen), SIAM J. Math. Anal. 37(2006), no 5, pp 1371-1395

``Potential Theory for Shock Reflection by a Large-Angle Wedge'', (with G.-Q. Chen), Proc. Natl. Acad. Sci. USA, 102(2005), no. 43, pp. 15368--15372,

"Exact self-similar solutions for the two-dimensional plasma-ion sheath system", (with S.-Y. Ha and M. Slemrod).
J. Phys. A 38 (2005), no. 32, pp. 7197--7204.

``A geometric level-set formulation of a plasma-sheath interface'' (with S.-Y. Ha and M. Slemrod).
Short version (pdf file), Arch. Ration. Mech. Anal., 178(2005), no 1, pp 81 - 123
Full version (pdf file).

``Free Boundary Problems and Transonic Shocks for the Euler Equations in unbounded domains'' (with G.-Q. Chen), Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2004), no. 4, pp 827-869.

"Nonlinear functionals of multi-D discrete velocity Boltzmann equations" (with S.-Y. Ha), J. Statist. Phys. 114(2004), No 3-4, pp 1015-1033

``Existence and Stability of Multidimensional Transonic Shocks for the Euler Equations for Steady Potential Fluids in Unbounded Domains'' (with G.-Q. Chen), Hyperbolic problems: theory, numerics, applications, 419--432, Springer, Berlin, 2003.

``Steady Transonic Shocks and Free Boundary Problems in Infinite Cylinders for the Euler Equations'' (with G.-Q. Chen), Comm. Pure Appl. Math. 57(2004), No. 3 , pp 310 - 356

``Rotationally symmetric shrinking and expanding gradient Kahler-Ricci solitons'' (with T. Ilmanen and D. Knopf), J. Differential Geom., 65(2003), 169-209

``Constructing Convex Solutions via Perron's Method'' (with J. McCuan), Ann. Univ. Ferrara Sez. VII Sci. Mat. 53 (2007), no. 1, 65--94.

``Multidimensional Transonic Shocks and Free Boundary Problems for Nonlinear Equations of Mixed Type'' (with G.-Q. Chen),
J. Amer. Math. Soc. 16 (2003), 461-494.

``Monge's transport problem on a Riemannian manifold'' (with R. J. McCann), Trans. Amer. Math. Soc. 354 (2002), 1667-1697.

``Nonlocal geometric expansion of convex planar curves'', (with B. Andrews), J. Differential Equations. 182(2002), No. 2, 298-343.

``Uniqueness and transport density in Monge's mass transportation problem'' (with R. J. McCann), Calc. Var. Partial Differential Equations, 15 (2002) 1, 81-113.

``Constructing optimal maps for Monge's transport problem as a limit of strictly convex costs'' (with L. A. Caffarelli and R. J. McCann), J. Amer. Math. Soc., 15(2002), no. 1, pp. 1--26.

``Regularity of Lipschitz free boundaries in two-phase problems for fully nonlinear elliptic equations'', Indiana Univ. Math. J., 50(2001), no. 3., pp. 1171 -- 1200

``Variational evolution problems and nonlocal geometric motion'', Arch. Ration. Mech. Anal. 146(1999), no. 3, 221--274.

``Growth of a sandpile around an obstacle'', Monge Ampere Equation: Applications to Geometry and Optimization, 55-78, Contemp. Math. 226, Amer. Math. Soc., Providence, RI, 1999.

``Fast/slow diffusion and collapsing sandpiles'' (with L. C. Evans and R. F. Gariepy), J. Differential Equations, 137(1997), no. 1, 166--209.

``Regularity for nonisotropic two-phase problems with Lipschitz free boundaries'', Differential Integral Equations, 10(1997), no. 6, 1171-1180.

``Partial regularity for harmonic maps of evolution into spheres'', Comm. Partial Differential Equations, 19(1994), 5\&6, p. 761-790.