• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.635-648
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• 2022

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.395-406
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• 2014

We study the following nonlinear problem $-div(w(x){\mid}{\nabla}u{\mid}^{p(x)-2}{\nabla}u)+{\mid}u{\mid}^{p(x)-2}u={\lambda}f(x,u)$ in ${\Omega}$ which is subject to Neumann boundary condition. Under suitable conditions on w and f, we give the existence of a positive infimum eigenvalue for the p(x)-Laplacian Neumann problem.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.55-69
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• 1999

In this paper we analyze the error estimates for a single-phase nonlinear Stefan problem with Neumann boundary conditions. We apply the modified Crank-Nicolson method to get the optimal order of error estimates in the temporal direction.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.999-1017
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• 2024

In this paper, we study the Neumann problem for the complex Hessian quotient equation ${\frac{{\sigma}_k({\tau}{\Delta}uI+{\partial}{\bar{\partial}u)}}{{\sigma}_l({\tau}{\Delta}uI+{\partial}{\bar{\partial}u)}}}={\psi}$ with 0 ≤ 𝑙 < k ≤ n. We prove a priori estimate and global C¹ estimates, in particular, we use the double normal second derivatives on the boundary to establish the global C² estimates and prove the existence and the uniqueness for the Neumann problem of the above complex Hessian quotient equation.

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1315-1325
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• 2021

In this paper, we firstly prove some general inequalities for the Neumann eigenvalues for domains contained in a Euclidean n-space ℝⁿ. Using the general inequalities, we can derive some new Neumann eigenvalues estimates which include an upper bound for the (k + 1)^th eigenvalue and a new estimate for the gap of the consecutive eigenvalues. Moreover, we give sharp lower bound for the first eigenvalue of two kinds of eigenvalue problems of the biharmonic operator with Navier boundary condition on compact Riemannian manifolds with boundary and positive Ricci curvature.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.189-195
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• 2015

The goal of this note is to provide a detailed proof for local boundedness estimate near the boundary for weak solutions for second order elliptic equations with bounded measurable coefficients subject to Neumann boundary condition.

• East Asian mathematical journal
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• v.39 no.3
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• pp.305-317
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• 2023

We establish the existence and uniqueness of Green functions in Lipschitz domains for stationary Stokes systems with Neumann boundary conditions. For the uniqueness, we impose a different normalization condition from that in Choi et al. (J. Math. Fluid Mech., 20(4):1745-1769, 2018).

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.353-361
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• 2007

In this paper, we prove the existence of multiple solutions for Neumann and periodic problems. Our main tools are recent general multiplicity theorems proposed by B. Ricceri.

• Bulletin of the Korean Mathematical Society
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• v.35 no.2
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• pp.345-362
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• 1998

We introduce and anlyze a naturally parallelizable frequency-domain method for parabolic problems with a Neumann boundary condition. After taking the Fourier transformation of given equations in the space-time domain into the space-frequency domain, we solve an indefinite, complex elliptic problem for each frequency. Fourier inversion will then recover the solution of the original problem in the space-time domain. Existence and uniqueness of a solution of the transformed problem corresponding to each frequency is established. Fourier invertibility of the solution in the frequency-domain is also examined. Error estimates for a finite element approximation to solutions fo transformed problems and full error estimates for solving the given problem using a discrete Fourier inverse transform are given.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.405-413
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• 2001

The inverse boundary value problem for the steady state heat equation with convection term is considered in a simply connected bounded domain with smooth boundary. Taking the Dirichlet to Neumann map which maps the temperature on the boundary to the that flux on the boundary as an observation data, the global uniqueness for identifying the convection term from the Dirichlet to Neumann map is proved.