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Selected Publications

研究方向: 偏微分方程,变分方法,超导、液晶、电磁场的数学理论


Selected Publications

Citations in the American Mathematical Society MathSciNet

超导数学文献(分类号 82D55

[78]     Div-curl system with potential and Maxwell-Stokes system with natural boundary condition, submitted.

[77]     Remarks on magnetic fields with interior singularities, submitted (with A. Kachmar)

[76]     General magneto-static model, submitted.

[75]     Singular limits of anisotropic Ginzburg-Landau functional, J. Elliptic and Parabolic Equations, special issue dedicated to the 70th birthday of Prof. M. Chipot, 6 (1) (2020), 27-54.

[74]     Variational and operator methods for Maxwell-Stokes systems, Disc. Contin. Dyn. Systems, Ser. A, special issue dedicated to the 70th birthday of Prof. Wei-Ming Ni, 40 (6) (2020), 3909-3955.

[73]     Anisotropic nematic liquid crystals in an applied magnetic field, Nonlinearity, 33 (5) (2020), 2035-2076 (with S.J. Kim).

[72]     Discontinuous nonlinearity and finite time extinction, SIAM J. Math. Anal., 52 (1) (2020), 894-926 (with J.W. Chung, Y.J. Kim amd O.S. Kwon).

[71]     Superconductivity and the Aharonov-Bohm effect, C. R. Acad. Sci. Paris, Ser. I, 357 (2019), 216-220. (with A. Kachmar)

[70]     Concentration behavior and lattice structure of surface superconductivity , Mathematical Physics, Analysis and Geometry, 22 (2) (2019), article no. 12, 33 pages.  (with S. Fournais and J.-P. Miqueu)

 arXiv:1805.06010, 2018.

[69]     Existence, regularity and uniqueness of weak solutions to a quasilinear Maxwell system, Nonlinearity, 32 (9) (2019), 3342-3366 (with Zhibing Zhang).

[68]     Meissner states of type II superconductors, J. Elliptic and Parabolic Equations4 (2) (2018), 441-523.

DOI 10.1007/s41808-018-0027-0

Springer Nature Sharedit initiative link

[67]     超导与液晶边界层现象的数学问题 Mathematical problems of boundary layer behavior of superconductivity and liquid crystals),中国科学:数学(中文版)48 1期,庆贺董光昌教授90华诞专辑,83-110页,2018年。

[66]    Quasilinear systems involving Curl, Proc. Royal Soc. Edinburgh, Ser. A, 148  (2) (2018), 243-279 (with J. Chen)

[65]     Existence of surface smectic states of liquid crystals, J. Functional Analysis, 274 (3) (2018), 900-958. (with A. Kachmar and S. Fournais)  

[64]     Directional curl spaces and applications to the Meissner states of anisotropic superconductors, J. Math. Phys., 58 (1) (2017), article no. 011508, 24 pages.

[63]      Mixed normal-superconducting states in the presence of strong electric currents, Archive for Rational Mechanics and Analysis, 223 (2017), 419-462. (with Y. Almog and B. Helffer)

[62]     Existence and regularity of solutions to quasilinear systems of Maxwell type and Maxwell-Stokes type, Calculus of Variations and PDEs, 55 (6) (2016), 1-43.

[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].

[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 J. Chen)     

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

[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 dedicated to the 60th birthday of Prof. Peter Bates, 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.  



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