• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.731-770
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• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• Journal of the Korean Mathematical Society
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• v.46 no.3
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• pp.609-620
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• 2009

We establish some estimates on the hyper bilinear Hilbert transform on both Euclidean space and torus. We also use a transference method to obtain a Kenig-Stein's estimate on bilinear fractional integrals on the n-torus.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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• pp.605-616
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• 2000

We prove the non-homogeneous boundary value problem for population evolution equations is well-posed in Sobolev space H(sup)3/2,3/2($\Omega$). It provides a strictly mathematical basis for further research of population control problems.

• East Asian mathematical journal
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• v.38 no.1
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• pp.129-141
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• 2022

We obtain interior regularity estimates in the weighted Orlicz spaces for viscosity solutions of fully nonlinear uniformly parabolic equations u_t - F(D² u, x, t) = f(x, t) in Q₁ under relaxed structure conditions on the nonlinear operator F.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.935-950
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• 1997

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

• Journal of the Korean Mathematical Society
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• v.54 no.6
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• pp.1801-1816
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• 2017

We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol g on the Fock-Sobolev spaces ${\mathcal{F}}^p_{{\psi}m}$. We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ if and only if g is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of g being not bigger than one. We also identified all those positive numbers p for which the operator $V_g$ belongs to the Schatten $S_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of g.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.533-546
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• 2018

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

• Journal of Astronomy and Space Sciences
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• v.10 no.2
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• pp.146-151
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• 1993

AZ Cas는 B형의 주계열 별과 확장 대기를 가진 만기형으로 이루어진 쌍성계이다. 근성점 근처에서 Roche lobe를 채운 초거성으로부터 일어나는 질량 흐름이 미치는 효과를 구하기 위해 궤도위상 0.05와 0.09에서 불투명도 계수에 따른 AZ Cas의 선윤곽을 계산하였다. 원천 함수는 Hempe(1982)의 방법을 따라 Sobolev 근사방법을 이용하였으며 불투명도 계수가 클수록 넓은 흡수 부분을 가진 강한 선윤곽을 보였다. 궤도 위상 0.05의 부분식이세 나타난 bump는 흡수선위에 포피의 산란에 의해 생긴 방출선이 중첩되어 나타난 재방출 효과인 것으로 설명된다.

• Honam Mathematical Journal
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• v.24 no.1
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• pp.67-73
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• 2002

In this paper we discuss on the existence of general solution of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z})+G(z,\;w,\;\bar{w})$ in the Sololev Space $W_{1,p}(D)$, that is generalization of a first order Non-linear Elliptic System of Partial Differential Equations $\frac{{\partial}w}{{\partial}\bar{z}}=F(z,\;w,\;\frac{{\partial}w}{{\partial}z}).$

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1205-1234
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• 2001

We consider the time local well-posedness of the Benjamin equation. Like the result due to Keing-Ponce-Vega [10], [12], we show that the initial value problem is time locally well posed in the Sobolev space H$^{s}$ (R) for s>-3/4.