• Journal of the Chungcheong Mathematical Society
• /
• v.32 no.2
• /
• pp.239-243
• /
• 2019

Logarithmic Sobolev trace inequalities are derived from the well known classical Sobolev trace inequalities as a limiting case.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.2
• /
• pp.301-305
• /
• 2020

Logarithmic fractional Sobolev trace inequalities are derived as a generalization of the results in [6, 9].

• Journal of the Korean Mathematical Society
• /
• v.61 no.2
• /
• pp.341-356
• /
• 2024

In this paper, apply the regularities of the fractional Poisson kernels, we establish the Sobolev type trace inequalities of homogeneous Besov spaces, which are invariant under the conformal transforms. Also, by the aid of the Carleson measure characterizations of Q type spaces, the local version of Sobolev trace inequalities are obtained.

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

Sobolev trace inequalities on nonhomogeneous fractional Sobolev spaces are established.

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

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

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

• Journal of applied mathematics & informatics
• /
• v.4 no.2
• /
• pp.433-446
• /
• 1997

In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.

• Journal of applied mathematics & informatics
• /
• v.4 no.1
• /
• pp.167-178
• /
• 1997

In this paper we present an application to airfoil design of an optimum design method based on optimal control theory. The method used here transforms the design problem by way of a change of variable into an optimal control problem for a distributed system with Neumann boundary control. This results in a set of variational inequalities which is solved by adding a penalty term to the differential equation. This si inturn solved by a finite element method.

• Journal of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.401-418
• /
• 2021

For complete manifolds with α-Bach tensor (which is defined by (1.2)) flat, we provide some rigidity results characterized by some point-wise inequalities involving the Weyl curvature and the traceless Ricci curvature. Moveover, some Einstein metrics have also been characterized by some $L^{\frac{n}{2}}$-integral inequalities. Furthermore, we also give some rigidity characterizations for constant sectional curvature.