## 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), to appear in Arch. Ration. Mech. Anal.

**
``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.