Works

Selected Publications

[63] Existence of surface smectic states of liquid crystals, submitted, https://arxiv.org/submit/1486478 (with A. Kachmar and S. Fournais)

[62] Mixed normal-superconducting states in the presence of strong electric currents, submitted (with Y. Almog and B. Helffer)

[61] Regularity of weak solutions to nonlinear Maxwell systems, J. Math. Phys., 56 (2015), 071508.

[60] A brief introduction on some mathematical problems of surface superconductivity (关于表面超导的若干数学问题）, Sciencepaper Online中国科技论文在线，[2015-03-03]. http://www.paper.edu.cn/releasepaper/content/201503-2.

[59] Partial Sobolev spaces and anisotropic smectic liquid crystals, Calculus of Variations and PDEs, 51 (2014), 963-998.

[58] An extended magnetostatic Born-Infeld model with a concave lower order term, J. Math. Phys., 54 (2013), 111501 (with Jun Chen)

[57] Functionals with operator curl in an extended magnetostatic Born-Infeld model, SIAM J. Math. Anal., 45 (4) (2013), 2253-2284. (with Jun Chen)

[56] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field, Transactions of Amer. Math. Soc., 365(3) (2013), 1183-1217. (with Yaniv Almog and Bernard Helffer)

[55] Phase transition for potential with higher dimensional wells, Communications on Pure and Applied Mathematics, 65 (6)(2012), 833-888， (with Fanghua Lin and Changyou Wang)

[54] Superconductivity near the normal state in a half-plane under the action of a perpendicular electric current and an induced magnetic field, part II : the large conductivity limit, SIAM J. Math. Anal., 44(6) (2012), 3671-3733. (with Yaniv Almog and Bernard Helffer)

[53] On a quasilinear system arising in the theory of superconductivity, Proc. Royal Soc. Edinburgh, vol. 141 A (2011), 397-407, (with Gary Lieberman)

[52] Asymptotics of solutions of a quasilinear system involving curl, J. Math. Phys., vol. 52 (2011), article no. 023517, 34pp.

[51] Superconductivity near the normal state under the action of electric currents and induced magnetic fields in R^2, Comm. Math. Phys., vol. 300, no.1 (2010), 147-184. (with Yaniv Almog and Bernard Helffer)

[50] A Note on best Sobolev and relative iso-perimetric constants and Neumann problems in exterior domains （关于最佳索伯列夫常数和相对等周常数及外区域纽曼问题的注）, Sciencepaper Online 中国科技论文在线 [2010-02-17]. http://www.paper.edu.cn/releasepaper/content/201002-495（with Xuefeng Wang）.

[49] Remarks on nodal sets of equations with magnetic Schrodinger operators (含有磁Schrodinger算子的偏微分方程复值解的零点集), Sciencepaper Online中国科技论文在线 [2010-03-01]. http://www.paper.edu.cn/releasepaper/content/201003-17.

[48] Minimizing Curl in a multiconnected Domain, J. Math. Phys., vol. 50, no. 3, (2009), art. no. 033508.

[47] On a quasilinear system involving the operator Curl, Calculus of Variations and PDE, vol. 36, no. 3 (2009), 317-342.

[46] An eigenvalue variation problem of magnetic Schrodinger operator in three-dimensions, Disc. Contin. Dyn. Systems, special issue for Peter Bates’ 60th birthday, vol. 24, no. 3 (2009), 933-978.

[45] A three-stage operator-splitting/ finite element method for the numerical simulation of liquid crystal flow, International Journal of Numerical Analysis and Modeling, vol. 6, no. 3 (2009), 440-454. (with R.Glowinski and P. Lin)

[44] Nucleation of instability of Meissner state of superconductors and related mathematical problems, in: B. J. Bian, S. H. Li and X. J. Wang eds., Trends in Partial Differential Equations, for Prof Guangchang Dong’s 80th birthday, “Advanced Lectures in Mathematics”, ALM10, pp.323-372, Higher Education Press and International Press, Beijing-Boston, 2009.

[43] Reduced Landau-de Gennes functional and surface smectic state of liquid crystals, Journal of Functional Analysis, vol. 255, no. 11 (2008), 3008-3069. (with B. Helffer)

[42] Critical elastic coefficient of liquid crystals and hysteresis, Comm. Math. Phys., vol. 280, no.1, (2008), 77-121.

[41] Nucleation of instability in Meissner state of 3-dimensional superconductors, Comm. Math. Phys., vol. 276, no. 3, (2007), 571-610. (with P. Bates)

[40] Analogies between superconductors and liquid crystals: nucleation and critical fields, in: Asymptotic Analysis and Singularities, Advanced Studies in Pure Mathematics, Mathematical Society of Japan, Tokyo, vol.47-2 (2007); pp. 479-517.

[39] Nodal set of solutions of equations involving magnetic Schrodinger operator in three dimensions, J. Math. Phys., vol. 48, no. 5, (2007), article number 053521.

[38] Magnetic field-induced instabilities in liquid crystals, SIAM J. Math. Anal., vol. 38, no. 5 (2007), 1588-1612, (with F. H. Lin)

[37] Landau-de Gennes model of liquid crystals with small Ginzburg-Landau parameter, SIAM J. Math. Anal., vol.37, no.5 (2006), 1616-1648.

[36] Multiple states and hysteresis for type I superconductors, J. Math. Phys.,vol.46, no.7 (2005), Article no. 073301. (with Yihong Du).

[35] Surface superconductivity in 3-dimensions, Trans. Amer. Math. Soc., vol. 356 (10) (2004), 3899-3937.

[34] Landau-de Gennes model of liquid crystals and critical wave number, Comm. Math. Phys., vol. 239 (1-2) (2003), 343-382.

[33] Superconductivity near critical temperature, J. Math. Phys., vol. 44 (6) (2003), 2639-2678.

[32] Superconducting films in perpendicular fields and effect of de Gennes parameter, SIAM J. Math. Anal., vol. 34 (4) (2003), 957-991.

[31] An operator-splitting method for liquid crystal model, Comp. Phys. Comm., vol. 152 (3) (2003), 242-252, (with R. Glowinski and P. Lin)

[30] Upper critical field and location of surface nucleation of superconductivity, Ann. LHP Analyse Non Lineaire, vol. 20 (1), 2003, 145-181. (with B. Helffer)

[29] Surface superconductivity in applied magnetic fields above H_c2, Comm. Math. Phys., vol. 228 (2), (2002), 327-370.

[28] Upper critical field for superconductors with edges and corners, Calculus of Variations and PDE, vol. 14 (4) (2002), no. 4, 447-482.

[27] On a problem related to vortex nucleation of superconductivity, J. Differential Equations, vol. 182 (2002), 141-168. (with K. H. Kwek)

[26] Schrodinger operators with non-degenerately vanishing magnetic fields in bounded domains, Trans. Amer. Math. Soc., vol. 354 (10) (2002), 4201-4227. (with K. H. Kwek)

[25] Ginzburg-Landau system and surface nucleation of superconductivity, Methods and Applications of Analysis, vol. 8 (2) (2001), 279-300. (with K. Lu)

[24] Surface nucleation of superconductivity in 3-dimension, J. Differential Equations, vol. 168 (2) (2000), 386-452. (with K. Lu)

[23] Asymptotics of minimizers of variational problems involving curl functional, J. Math. Phys., vol. 41 (7) (2000), 5033-5063. (with Y. Qi)

[22] Gauge invariant eigenvalue problems in R^2 and in R^2_+, Trans. Amer. Math. Soc., vol. 352 (3) (2000), 1247-1276. (with K. Lu)

[21] Estimates of the upper critical field for the Ginzburg-Landau equations of superconductivity, Physica D, vol. 127 (1-2) (1999), 73-104. (with K. Lu)

[20] Eigenvalue problem of Ginzburg-Landau operator in bounded domains, J. Math. Phys., vol. 40 (6) (1999), 2647-2670. (with K. Lu)

[19] Yamabe problem on half spaces, Nonlinear Anal. TMA, vol. 37 (2) (1999), 161-186. (with G. Bianchi)

[18] A variational problem of liquid crystals, Comm. in Applied Nonlinear Anal., vol. 5 (1) (1998), 1-31. (with Y. Yi)

[17] Semilinear Neumann problem in an exterior domain, Nonlinear Anal. TMA, vol. 31 (7) (1998), 791-821. (with X. Wang)

[16] Ginzburg-Landau equation with De Gennes boundary conditions, J. Differential Equations, vol. 129 (1) (1996), 136-165. (with K. Lu)

[15] Least energy solutions of semilinear Neumann problems in R^4 and asymptotics, J. Math. Anal. Appl., vol. 201 (2) (1996), 532-554. (with X. Xu)

[14] Singular limit of quasilinear Neumann problems, Proc. Royal Soc. Edinburgh, vol. 125A (1) (1995), 205-223.

[13] Further study on the effect of boundary conditions, J. Differential Equations, vol. 117 (2) (1995), 446-468.

[12] Condensation of least-energy solutions: The effect of boundary conditions, Nonlinear Anal. TMA, vol. 24 (2) (1995), 195-222.

[11] Condensation of least-energy solutions of a semilinear Neumann problem, J. Partial Differential Equations, vol. 8 (1) (1995), 1-36.

[10] The Melnikov method and elliptic equations with critical exponent, Indiana Univ. Math. J., vol. 43 (3) (1994), 1045-1077. (with R. Johnson and Y. Yi)

[9] Singular solutions of the elliptic equation Delta u-u+u^p=0, Ann. Mat. Pura Appl., vol. 166 (4) (1994), 203-225. (with R. Johnson and Y. Yi)

[8] Positive solutions of super-critical elliptic equations and asymptotics, Comm. Partial Differential Equations, vol. 18 (5-6) (1993), 977-1019. (with R. Johnson and Y. Yi)

[7] Singular ground states of semilinear elliptic equations via invariant manifold theory, Nonlinear Anal. TMA, vol. 20 (11) (1993), 1279-1302. (with R. Johnson and Y. Yi)

[6] On an elliptic equation related to the blow-up problem of the nonlinear Schrodinger equation, Proc. Royal Soc. Edinburgh, vol. 123A (4) (1993), 763-782. (with R. Johnson)

[5] Positive solutions of the elliptic equation Delta u+u^{(n+2)/(n-2)}+K(x)u^q=0 in R^n and in balls, J. Math. Anal. Appl., vol. 172 (2) (1993), 323-338.

[4] Blow-up behavior of ground states of semilinear elliptic equations in R^n involving critical Sobolev exponents, J. Differential Equations, vol. 99 (1) (1992), 78-107. (with X. Wang)

[3] Singular behavior of least-energy solutions of a semilinear Neumann problem involving critical Sobolev exponents, Duke Math. J., vol. 67 (1) (1992), 1-20. (with W. M. Ni and I. Takagi)

[2] Positive solutions of Delta u+K(x)u^p=0 without decay conditions on K(x), Proc. Amer. Math. Soc., Vol. 115 (3) (1992), 699-710.

[1] Existence of singular solutions of a semilinear elliptic equation in R^n, J. Differential Equations, vol. 94 (1) (1991), 191-203.