Selected preprints and publications of Mikhail Feldman.
This material is based upon work supported by the National Science Foundation
under various grants.
``Regularity of Solutions to Regular Shock Reflection for Potential
Flow"
(with M. Bae and G.-Q. Chen), submitted
``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, 191--218.
``Global Solutions to Shock Reflection by Large-Angle Wedges for
Potential Flow''
(with G.-Q. Chen), to appear in Annals of Math.
``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,
``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
"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.