Xu-Jia Wang

Xu-Jia Wang (Chinese: 汪徐家; born September 1963) is a Chinese-Australian mathematician. He is a professor of mathematics at the Australian National University and a fellow of the Australian Academy of Science.

Biography

Wang was born in Chun'an County, Zhejiang province, China. Wang obtained his B.S. in 1983 and his Ph.D. in 1990 from the Department of Mathematics of Zhejiang University (ZJU) in Hangzhou.^[1]

After completing his PhD, Wang served as lecturer and associate professor, at ZJU before departing for ANU In 1995. Wang is a Professor in the Centre for Mathematics and its Applications and Mathematical Sciences Institute of Australian National University.

Wang is well known for his work on differential equations, especially non-linear partial differential equations and their geometrical and transportational applications. Australian mathematician Neil S. Trudinger is his longtime collaborator.

Honors and awards

Australian Mathematical Society Medal (2002)^[2]
invited speaker, 2002 International Congress of Mathematicians
Fellow of the Australian Academy of Science (2009).^[3]

Publications (selected)

Perfume & Copyright

(with Huaiyu Jian, Jian Lu) "Nonuniqueness of solutions to the Lp-Minkowski problem", Adv. Math. 281 (2015), 845-856.
(with Qirui Li, Filippo Santambrogio) "Regularity in Monge's mass transfer problem", J. Math. Pures Appl. 102 (2014), no. 6, 1015-1040.
(with Huaiyu Jian) “Optimal boundary regularity for nonlinear singular elliptic equations”, Adv. Math. 251 (2014), no. 30 January 2014, 111-126.
(with Huaiyu Jian) “Bernstein theorem and regularity for a class of Monge-Ampère equations”, J. Differential Geom. 93 (2013), no. 3, 431-469.
(with Jian Lu) “Rotationally symmetric solutions to the Lp-Minkowski problem”, Electron. J. Differential Equations 254 (2013), no. 3, 983-1005.
(with Gang Tian) “A priori estimates for fully nonlinear parabolic equations”, Int. Math. Res. Not. IMRN 2012 (2012), 1-21.
(with Bin Zhou) “On the existence and nonexistence of extremal metrics on toric Kähler surfaces”, Adv. Math. 226 (2011), no. 5, 4429-4455.
“Convex solutions to the mean curvature flow”, Ann. of Math. 173 (2011), no. 3, 1185-1239.
(with Aram Karakhanyan) “On the reflector shape design”, J. Differential Geom. 84 (2010), no. 3, 561-610.
(with Jiakun Liu, Neil Trudinger) "Interior C 2,alpha regularity for potential functions in optimal transportation", Comm. Partial Differential Equations 35 (2010), no. 1, 165-184.
(with Guji Tian) “Moser-Trudinger type inequalities for the Hessian equation”, J. Funct. Analysis 259 (2010), no. 8, 1974-2002.
(with Neil Trudinger) “The intermediate case of the Yamabe problem for higher order curvatures”, Int. Math. Res. Not. IMRN 227 (2010), 1-22.
(with Weimin Sheng) “Singularity profile in the mean curvature flow”, Methods and Applications of Analysis 16 (2009), no. 2, 139 - 155.
(with Neil Trudinger) “On Harnack inequalities and singularities of admissible metrics in the Yamabe problem”, Calc. Var. Partial Differential Equations 35 (2009), no. 3, 317-338.
(with Neil Trudinger) “On strict convexity and continuous differentiability of potential functions in optimal transportation”, Arch. Ration. Mech. Anal. 192 (2009), no. 3, 403-418.
(with Neil Trudinger) “On the second boundary value problem for Monge-Ampere type equations and optimal transportation”, Ann. Sc. Norm. Super. Pisa 8 (2009), no. 1, 143-174.
(with Neil Trudinger) “Quasilinear Elliptic Equations with Signed Measure Data”, Discrete Contin. Dyn. Syst. Ser. A 23 (2009), no. 1 & 2, 477-494.
(with Neil Trudinger) “Boundary regularity for the Monge-Ampere and affine maximal surface equations”, Ann. of Math. 167, no. 3, 993-1028.
(with Huaiyu Jian) “Continuity estimates for the Monge-Ampere equation”, SIAM J. Math. Anal. 39 (2007), no. 2, 608-626.
(with Weimin Sheng, Neil Trudinger) “The Yamabe problem for higher order curvatures”, J. Differential Geom. 77 (2007), 515-553.
(with Kai-Seng Chou) “The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry”, Adv. Math. 205 (2006), 33-83.
“A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry”, Chin. Ann. Math. Ser. B 27 (2006), 169-178.
“Schauder estimates for elliptic and parabolic equations”, Chin. Ann. Math. Ser. B 27B (2006), no. 6, 637-642.
(with Neil Trudinger) “The affine Plateau problem”, J. Amer. Math. Soc. 18 (2005), no. 2, 253-289.
(with Neil Trudinger, Xi-Nan Ma) 2005, “Regularity of Potential Functions of the Optimal Transportation Problem”, Arch. Ration. Mech. Anal. 177 (2005), 151-183.
(with Nina Ivochkina, Neil Trudinger) “The Dirichlet Problem for degenerate Hessian Equations”, Comm. Partial Differential Equations, 29 (2004), 219-235.
(with Nina Ivochkina, Neil Trudinger) “The Dirichlet Problem for Degenerate Hessian Equations”, Comm. Partial Differential Equations, 29 (2005), no. 1&2, 219-235.
(with Weimin Sheng, John Urbas) “Interior curvature bounds for a class of curvature equations”, Duke Math. J. 123 (2004), no. 2, 235-264.
(with Xiaohua Zhu) “Kähler-Ricci solitons on toric manifolds with positive first Chern class”, Adv. Math. 188 (2004), 87-103.
“On the design of a reflector antenna 2”, Calc. Var. Partial Differential Equations 20 (2004), 329-341.
(with Neil Trudinger) “Affine complete locally convex hypersurfaces”, Invent. Math. 150 (2002), 45-60.
(with Neil Trudinger) “Bernstein-Jorgens Theorem for a Fourth Order Partial Differential Equation”, J. Partial Differential Equations 15 (2002), no. 1, 78-88.
(with Neil Trudinger) “Hessian Measures III”, J. Funct. Analysis 193 (2002), 1-23.
(with Neil Trudinger) “On locally convex hypersurfaces with boundary”, J. Reine Angew. Math. 551 (2002), 11-32.
(with Neil Trudinger) “On the weak continuity of Elliptic Operators and applications to Potential Theory”, Amer. J. Math 124 (2002), no. 2, 369-410.
(with Kai-Seng Chou) “A variational theory of the Hessian equation”, Comm. Pure Appl. Math. 54 (2001), 1029-1064.
(with Neil Trudinger) “On the Monge mass transfer problem”, Calc. Var. Partial Differential Equations 13 (2001), 19-31.
(with Neil Trudinger) “The Bernstein problem for affine maximal hypersurfaces”, Invent. Math. 140 (2000), no. 2, 399 - 422.
(with Pengfei Guan, Neil Trudinger) “On the Dirichlet problem for degenerate Monge-Ampère equations”, Acta Math 182 (1999), no. 1, 87-104.
(with Neil Trudinger) “Hessian Measures II”, Ann. of Math. 150 (1999), no. 2, 79-604.
"Neumann problems of semilinear elliptic equations involving critical Sobolev exponents", J. Differential Equations 93 (1991), no. 2, 283-310.

References

External links

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