・論文

- [86] Aramaki, J. : Variational inequality in a curl constraint problem, to appear in Journal of Nonlinear and Convex Analysis.
- [85] Aramaki, J. : Coupled variational problem associated with the Bean critical-state model in type II superconductors with thermal effect, Advences in Differential Equations and Cotroll Processes, Vol. 19, No. 2, (2018), 101-126.
- [84] Aramaki, J. : Existence of the solution of a coupled variational problem constraint by a function depending on the solution, International Journal of Functional Analysis, Operator Theorry and Applications, Vol. 10, No. 1, (2018), 33-59.
- [83] Existence of weak solution for a class of abstract coupling system associated with stationary electromagnetic system, Taiwanese Journal of Mathematics, Vol. 22, No.3, (2018), 741-765.
- [82] Aramaki, J. : Variational problem involving operator curl assosiated with $p$-curl system, Turkish Jounral of Mathematics, Vol. 42, No. 3, (2018), 949-966.
- [81] Aramaki, J. : Existence of a solution to a quasivatiational inequality with a perturbation term, Advances in Differential Equations and Control Processes, Vol. 18, No. 1, (2017), 39-54.
- [80] Aramaki, J. : A note on the existence of the solution of a coupled variational problem, International Journal of Functional Analysis, Operator Theory and Applications, Vol. 9, No. 1, (2017), 17-29.
- [79] Aramaki, J. : Variational inequality with evolutionary curl constraint in a multi-connected domain, Communications in Mathematical Analysis, Vol. 20, No. 1, (2017), 1-26.
- [78] Aramaki, J. : Minimizing the $L^p$ norm of curl in a multiconnected domain, International Journal of Mathematics, Vol. 28, No. 1, (2017), 1750004 1-12 .
- [77] Aramaki, J. : Existence of weak solutions for a class of stationary electromagnetic coupling system, Advances in Differential Equations and Control Processes, Vol. 17, No. 4, (2016), 301-320.
- [76] Aramaki, J. : Existence of weak solutions for a class of abstract coupling system containing stationary electromagnetic system , International Journal of Functional Journal, Operator Theory and Applications, Vol. 8, No. 1-3, (2016), 23-50.
- [75] Aramaki, J. : Variational problem involving operator curl in a multi-connected domain, Chinese Journal of Mathematics, ID 2459694, (2016), 1-8.
- [74] Aramaki, J. : Quasilinear parabolic type equation arising in electromagnetism in a multi-connected domain, Internatonal Journal of Evolution Equations, Vol. 10, No. 2, (2016), 119-144.
- [73] Aramaki, J. : Poincar\'e inequality and Campanato estimaes for weak solutions of a parabolic equation, Electronic Journal of Differential Equations, Vol. 2016, No. 204, (2016), 1-8.
- [72] Aramaki, J. : Existence of solutions for a quasilinear parabolic type equation containing $p$-curl system and applications to blow-up and extinction, Advances in Differential Equations and Control Processes, Vol. 17, No. 2, (2016), 117-158.
- [71] Aramaki, J. : Regularity of weak solution for a quasilinear parabolic type equation associated with the Maxwell equation, Far East Journal of Mathematical Sciences, Vol. 100, No. 3, (2016), 505-520.
- [70] Aramaki, J., : On a degenerate evolution system associated with the Bean critical-state for type II superconductors, Abstract and Applied Analysis, Vol. 2015, ID 875190, 1-13..
- [69] Aramaki, J. : A note on the stability of the twisted nematic critical state in the liquid crystal theory, Far East Journal of Mathematical Sciences, Vol. 97, No. 8, (2015), 959-968.
- [68] Aramaki, J. : Existence and uniqueness of a classical solution for a quasilinear parabolic type equation associated with the Maxwell equation, International Journal of Evolution Equations, Vol. 9, No. 3, (2015), 277-298.
- [67] Aramaki, J., Chinen, K., Ito, Y. and Ono, S. : The effect of magnetic fields with specific boundary data in the theory of liquid crystals, Methods and Applications of Analysis, Vol. 22, No. 3, (2015), 313-342.
- [66] Aramaki, J. : On the H\"older continuity with exponent $(1+\alpha)/2$ in the time variable of solutions of parabolic equations, Electronic Journal of Differential Equations, Vol. 2015, No. 96, (2015), 1-6.
- [65] Aramaki, J. : Regularity of weak solutions for degenerate quasilinear elliptic equations involving operator curl, Journal of Mathematical Analysis and Applications, .Vol. 426, (2015), 872-892.
- [64] Aramaki, J. : Stability and asymptotics in nematic liquid crystals under a small Dirichlet data and a non-constant magnetic field, Physica D: Nonlinear Phenomena, Vol. 290, (2015), 1-7.
- [63] Aramaki, J. : On the classical solutions of the extended magnetostatic Born-Infeld system with a concave lower order term, Applied Mathematical Sciences, Vol. 8, No. 58, (2014), 2871-2916.
- [62] Aramaki, J. On the classical solutions of the extended magnetostatic Born-Infeld system, Applied Mathematical Sciences, Vol. 8, No. 49, (2014), 2397-2426.
- [61] Aramaki, J. : Asymptotic behavior of nematic state in the theory of
liquid crystal with specific boundary data under a tilted magnetic field,
Applied Mathematical Sciences, Vol. 8, No. 23, (2014), 1109-1126.

- [60] Aramaki, J. : $L^p$ theory for the div-curl system, International Journal of Mathematical Analysis, Vol. 8, No. 6, (2014), 259-271.
- [59] Aramaki, J. : Another proof of the regularity for harmonic maps from a Riemannian manifold into the unit sphere, Electronic Journal of Differential Equations, Vol. 2014, No. 34, (2014), 1-7.
- [58] Aramaki, J. : Variational problems and asymptotic behaviors associated with liquid crystals, International Math. Forum, Vol. 8, No. 40, (2013), 1985-1997.
- [57] Aramaki, J., Quasilinear systems associated with superconductivity, Electronic Journal of Differrential Equations, Vol. 2013, No. 190, (2013), 1-22.
- [56] Aramaki, J. : A remark on harmonic maps into the unit sphere, Nonlinear Analysis and Differential Equations, Vol. 1, No. 4. , (2013), 149-157.
- [55] Aramaki, J. : Regularity of weak solutions for a quasilinear elliptic system in three-dimensional space associated with superconductivity, Far East J. Math. Sci., Vol. 76, No. 1, (2013), 175-197.
- [54] Aramaki, J. : Magnetic field-induced stability of a specific configuration and the asymptotic behavior of minimizers in nematic liquid crystals, Turkish J. Math., Vol. 37, No. 6, (2013), 1001-1021.
- [53] Aramaki, J. : Asymptotic behavior of nematic state with specific boundary data under a tilted magnetic field, Far East J. Math. Sci. Vol. 71, No.1, (2012), 1-20.
- [52] Aramaki, J. : The Freedericksz transition in nematic liquid crystals, J. Partial Differential Equations, Vol. 25, No. 3, (2012), 276-294.
- [51] Aramaki, J. : Weak stability of a critical twisted nematic state under the magnetic field in liquid crystals, International J. Pure Appl. Math., Vol. 78, No. 2, (2012), 197-206.
- [50] Aramaki, J. : The effect of external field in the theory of liquid crystals, Tokyo J. Math., Vol. 35, No. 1, (2012), 181-211.
- [49] Aramaki, J., Chinen, K. and Kato, M. : Asymptotics of minimizers of variational problems in a multi-connected domain associated with the theory of liquid crystal, Taiwanese J. Math., Vol. 16, No. 2, (2012), 561-578.
- [48] Aramaki, J. and Chinen, K. : The effect of non-constant external fields in the theory of liquid crystals,International Mathematical Forum, Vol. 7, No. 14, (2012), 639-667.
- [47] Aramaki, J.: Quasilinear elliptic system in a three-dimensional space associated with superconductivity, Far East J. Math. Sci. (FJMS), Vol. 59, No. 1, (2011), 1-45.
- [46] Aramaki, J. : Asymptotic behavior of nematic states in the theory of liquid crystals under applied magnetic fields, Int. Math. Forum, Vol. 6, No. 36, (2011), 1763-1775.
- [45] Aramaki, J. : Critical elastic coefficients in the theory of liquid crystal, Int. J. Pure Appl. Math., Vol. 65, No. 2, (2010), 177-224.
- [44] Aramaki, J. : Estimate of the Hausdorff measure of singular set of a solution for a semi-linear elliptic equation associated with supeconductivity, Archivum Mathematicum (Brno), Vol. 46, No. 3, (2010), 185-201.
- [43] Aramaki, J. : Variational problems assocated with smectic-C to nematic or smectic-A to nematic phase transition in the theory of liquid crystals, Far East J. Math. Sci. (FJMS), Vol. 41, No. 2, (2010), 153-198.
- [42] Aramaki, J.: Erratum : On the variational problems in a multi-connected domain associated with the theory of liquid crystals, Int. J. Pure Appl. Math. Vol. 60, No. 2, (2010), 81-86..
- [41] Aramaki, J.: On the variational problems in a multi-connected domain associated with the theory of liquid crystals, Int. J. Pure Appl. Math., Vol. 58, No. 4, (2010), 453-472.
- [40] Aramaki, J. : Nodal sets and Singular sets of solutions for semi-linear elliptic equations associated with superconductivity, Far East J. Math. Sci. (FJMS), Vol. 38, No. 2, (2010), 137-179.
- [39] Aramaki, J. : Minimizing divergence in a multiconnected domain, Far East J. Math. Sci. (FJMS)., Vol. 38, No. 1, (2010), 65-84.
- [38] Aramaki, J. : Doubling property for solutions of a semi-linear elliptic equation associated with superconductivity, Int. J. Funct. Anal. Oper. Theory Appl., Vol. 1, No. 2, (2009), 97-114.
- [37] Aramaki, J. : A note on $A_p$ estimates for solutions of a semi-linear elliptic equation associated with superconductivity, Int. J. Pure Appl. Math., Vol. 55, No. 2, (2009), 257-264.
- [36] Aramaki, J., Nurumhamad, A. and Tomioka, S. : A note on a semi-linear elliptic problem with de Gennes boundary condition associated with the superconductivity, Far East J. Math. Sci. (FJMS), Vol. 32, No. 2, (2009), 153-167.
- [35] Aramaki, J. : A remark on a semi-linear elliptic problem with de Gennes boundary condition associated with the superconductivity, Int. J. Pure Appl. Math., Vol. 50, No. 1, (2009), 97-110.
- [34] Aramaki, J. : The Ginzburg-Landau model with the de Gennes boundary condition associated with the superconductivity, Far East J. Math. Sci. (FJMS), Vol. 31, No. 1, (2008), 143-180.
- [33] Aramaki, J. : On the asymptotic behavior of the ground state energy for a Schr\"odinger operator with the de Gennes boundary condition associated with the superconductivity, Int. J. Pure Appl. Math., Vol. 46, No. 3, (2008), 355-373.
- [32] Aramaki, J. : On an eigenvalue asymptotics for a Schr\"odinger operator with the de Gennes effect associated with superconductivity, Far East J. Math. Sci. (FJMS), Vol. 29, No. 1, (2008), 151-170..
- [31]. Ando, N., Aramaki, J. : A remark on the eigenvalue asymptotics associated with superconductivity near critical temperature, Int. J. Pure and Appl. Math., Vol. 40, No. 1, (2007), 123-134.
- [30]. Aramaki, J., Asymptotics of the eigenvalues for the Neumann Laplacian with non-constant magnetic field associated with superconductivity, Far East J. Math. Sci. (FJMS), Vol. 25, No. 3, (2007), 529-584.
- [29] Aramaki, J. : On an elliptic model with general nonlinearity associated with superconductivity, Int. J. Differ. Equ. Appl. Vol. 10, No. 4, (2005), 449--466 (2006).
- [28] Aramaki, J. : Upper critical field and location of surface nucleation for the Ginzburg-Landau system in non-constant applied field, Far East J. of Math. Sci. Vol. 23, No. 1, (2006), 89-125.
- [27] Aramaki, J. : On an elliptic problem with general nonlinearity associated with superheating field in the theory of superconductivity, Int. J. Pure and Appl. Math., Vol. 28. No. 1, (2006), 125-148.
- [26] Aramaki, J. : Asymptotics of eigenvalue for the Ginzburg-Landau operator in an applied magnetic fieldvanishing of higher order, Int. J. Pure and Appl. Math. Sci. Vol. 2, No. 2, (2005), 257-281.
- [25] Aramaki, J. : Asymptotics of upper critial field of a superconductor in applied magnetic field vanishing of higher order, Int. J. Pure and Appl. Math., Vol. 21, No. 2, (2005), 151-166.
- [24] Aramaki, J. : Semi-classical asymptotics of the ground state energy for the Neumann problem associated with superconductivity, Int. J. Diff. Equ. Appl., Vol. 9, No. 3, (2004), 239-271.
- [23] Aramaki, J. : Semi-classical asymptotics of the trace of the heat kernel for the Schr\"odinger operator with degenerate potential, Int. J. Pure and Appl. Math., Vol. 15, No. 1, (2004), 103--136.
- [22] Aramaki, J. : Semi-classical asymptotics of eigenvalues for the Dirac operator with magnetic and electric potentials, Int. J. Pure Appl. Math., Vol. 10, No. 3, (2004), 299--333.
- [21] Aramaki, J. Nurmuhammad, A. and Yamamoto, D. : Asymptotic behavior of the trace of the heat kernel for the magnetic Schr\"odinger operator, Advances in Math. Res. Vol. 3 (Ed. G. Oyibo), Nova Sci. Publ., Hauppauge, New York, (2003), 69--94.
- [20] Aramaki, J. : Eigenvalues asymptotics of self-adjoint operators on a Hilbert space and an application, Int. J. Pure and Appl. Math., Vol. 4, No. 3, (2003), 307--338.
- [19] Aramaki, J. : Semi-classical analysis for the eigenvalues of a Schr\"odinger operator with magnetic field, Asymptot. Anal., Vol. 29, No. 1, 39-68, (2002).
- [18] Aramaki, J. and Nurmuhammad, A. : Non-classical asymptotics of the trace of the heat kernel for the magnetic Schr\"odinger operator, Acta Math. Hungar. Vol. 94(1-2), 155-172, (2002).
- [17] Abe, M., Aramaki, J. and Nurmuhammad, A. : An example for the semi-classical analysis for the eigenvalues of a Schr\"odinger operator with magnetic field, Res. Activities, TDU. Vol. 23, No. 1, 3-14, (2001).
- [16] Aramaki, J. and Nurmuhammad, A. : A note on non-classical eigenvalue asymptotics, Hokkaido Math. J., Vol. 30, No. 2, 307-325, (2001).
- [15] Aramaki, J. : On the asymptotics of the trace of the heat kernel for the magnetic Schr\"odinger operator, Pacific J. Math., Vol. 198, No. 1, 1-14, (2001).
- [14] Aramaki, J. : Some remarks on semi-classical analysis for the eigenvalues of a Schr\"odinger operator with electro-magnetic wells, Japan. J. Math.,Vol. 26, No. 2, 321-353, (2000).
- [13] Aramaki, J. : Eigenvalues Asymptotics for a Class of Pseudodifferential Operators with a Parameter, Res. Activities, TDU, Vol. 21, No. 1, 3-27, (1999).
- [12] Aramaki, J. and Takahashi, H. : A note on the composition formula for pseudodifferential operators with a parameter, Res. Activities, TDU, Vol. 19, No. 1, 3-12, (1997).
- [11] Aramaki, J. : An extension of the Ikehara Tauberian theorem and its application, Acta Math. Hungar, Vol. 71(4), 297-326, (1996).
- [10] Aramaki, J. : On an extension of the Ikehara Tauberian theorem II, Tokyo J. Math. Vol. 18, No. 1, 91-110, (1995).
- [9] Aramaki, J. : Asymptotic behavior of eigenvalues for a class of pseudodifferential operators on R^n, Pacific J. Math. Vol. 156, No.1, 19-44, (1992).
- [8] Aramaki, J. : Complex powers of vector valued operators and its application to asymptotic behavior of eigenvalues, J. Funct.Anal., Vol. 87, No.2, 294-320, (1989).
- [7] Aramaki, J. : On an extension of the Ikehara Tauberian theorem, Pacific J. Math. Vol. 133, No. 1,13-30, (1988).
- [6] Aramaki, J. : Complex powers of a class of pseudodifferential operators in ${\mathbb R}^n$ and asymptotic behavior of eigenvalues, Hokkaido Math. J. Vol. XVI, No. 1, 1-28, (1987).
- [5] Aramaki, J. : On the asymptoric behavior of the spectrum of quasi-elliptic pseudodifferential operators on ${\mathbb R}^n$, Tokyo J. Math. Vol. 10, No.2, 481-505, (1987).
- [4] Aramaki, J. : Complex powers of a class of pseudodifferential operators and their applications, Hokkaido Math. J. Vol.XII, No.2, 199-225, (1983).
- [3] Aramaki, J. : Hypoellipticity for a class of pseudodifferential operators, Hokkaido Math. J. Vol. XI, No. 1, 15-28, (1982).
- [2] Aramaki, J. : On a class of pseudo-differential operators and hypoellipticity, Hokkaido Math. J. Vol IX, No. 2, 46-58, (1980).
- [1] Aramaki, J. : Some remarks on local solvability and hypoellipticity of second-order abstract evolution operator, Hokkaido Math. J. Vol. V, No. 2, 302-307, (1976).

・投稿中および準備中

.

Aramaki, J. : Existence and regularity of weak solution to a class of a
system containing a $p$-curl system in a multi-connected domain

Aramaki, J. : Existence of a weak solution to an evolution system and asymptotic behavior in a multi-connected domain

Aramaki, J. : Existence of a solution to a stationary quasi-variational
inequality in a multi-connected domain

Aramaki, J. : Existence of a weak solution to an evolution system and asymptotic behavior in a multi-connected domain

Aramaki, J. : Existence and regularity of a weak solution to a class of system in a multi-connected domain

Aramaki, J. : A version of the de Rham lemma

Aramaki, J. : Existence and regularity of weak solutions to the Poisson
equation with Neumann boundary condition and an application to the Maxwell-Stokes
type equation

Aramaki, J. : An application of a version of the de Rham lemma to the existence
of weak solution to the Maxwell-Stokes problem.

Aramaki, J. Existence of a weak solution to the stationary Maxwell-Stokes type system.

Aramaki, J. Existence of a weak solution to the Maxwell-Stokes type equation by the penalty method.

Preparation paper

Aramaki, J. Existence of a weak solution to the Maxwell-Stokes type equation with the Neumann boundary condition.