• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.287-291
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• 2009

A comparison of constants is given to show that a better constant for the Sobolev trace inequality can be obtained from the conjectured extremal function.

• Journal of the Chungcheong Mathematical Society
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• v.21 no.4
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• pp.493-499
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• 2008

We construct a minimizing sequence for the Sobolev trace inequality which satises compactness in the concentration compactness property.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1143-1149
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• 2020

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.583-586
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• 2011

A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.257-266
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• 1999

We used Carleson and Chang's method to give another proof of the Moser-Trudinger inequality which was known as a limiting case of the Sobolev imbedding theorem and at the same time we get sharper information for the bound.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.231-241
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• 2013

On the framework of the 2-adic group $\mathcal{Z}_2$, we study a Sobolev-like inequality where we estimate the $L^2$ norm by a geometric mean of the BV norm and the $\dot{B}_{\infty}^{-1,{\infty}}$ norm. We first show, using the special topological properties of the $p$-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space ˙$\dot{B}_1^{1,{\infty}}$. This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

• Korean Journal of Mathematics
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• v.6 no.2
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• pp.205-212
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• 1998

We investigate the behavior of $L^2$ harmonic one forms on complete manifolds and as an application, we show the space of $L^2$harmonic one forms on a complete Riemannian manifold of nonnegative Ricci curvature outside a compact set with bounded $n/2$-norm of Ricci curvature satisfying the Sobolev inequality is finite dimensional.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.3
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• pp.527-529
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• 2012

It is proved that the fractional Sobolev spaces $W^s_p(\mathbb{R}^n)$ 0 < $s$ < $n$, are compactly embedded into Lebesgue spaces $L^q(\Omega)$ for some bounded set $\Omega$­.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1341-1353
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• 2019

For complete Riemannian manifolds with vanishing Bach tensor and positive constant scalar curvature, we provide a rigidity theorem characterized by some pointwise inequalities. Furthermore, we prove some rigidity results under an inequality involving $L^{\frac{n}{2}}$-norm of the Weyl curvature, the traceless Ricci curvature and the Sobolev constant.