• Honam Mathematical Journal
• /
• v.43 no.1
• /
• pp.59-67
• /
• 2021

We characterize pluriharmonic symbols of the finite rank little Hankel operators on the Dirichlet space of the unit polydisk.

• Communications of the Korean Mathematical Society
• /
• v.12 no.2
• /
• pp.419-425
• /
• 1997

Consider a d-dimensional domain D that has finite Lebesque measure and a Dirichlet form which has discontinuous coefficient. Then the stationary Markov process corresponding to the given Dirichlet form is a semimartingale under suitable condition for D and the coefficient.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.319-331
• /
• 2019

On the weighted Dirichlet space, by the Sobolev's embedding theorem, we characterize the compactness for operators which are finite sums of products of several Toeplitz operators. Moreover, the essential spectrum of Toeplitz operator is characterized.

• Honam Mathematical Journal
• /
• v.41 no.3
• /
• pp.619-629
• /
• 2019

On the setting of the pluriharmonic Dirichlet space, we describe the essential norm of an operator which is a finite sum of products of several Toeplitz operators.

• Bulletin of the Korean Mathematical Society
• /
• v.60 no.1
• /
• pp.161-170
• /
• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

• 한국전산유체공학회:학술대회논문집
• /
• 2009.04a
• /
• pp.165-169
• /
• 2009

The effect of the Dirichlet boundary condition for the redistance equation of level set method on the solutionof sloshing problem is investigated by adopting four Dirichlet boundary conditions. For the solution of the incompressible Navier-Stokes equations, P1P1 four-step fractional finite element method is employed and a least-square finite element method is used for the solutions of the two hyperbolic type equations of level set method; advection and redistance equation. ALE (Arbitrary Lagrangian Eulerian) method is used to deal with a moving computational domain. It has been shown that the free surface motion in a sloshing tank is strongly dependent on the type of the Dirichlet boundary condition and the results of broken dam and sloshing problems using various Dirichlet boundary conditions are discussed and compared with the existing experimental results.

• Korean Journal of Mathematics
• /
• v.18 no.2
• /
• pp.201-211
• /
• 2010

We investigate the number of the nontrivial solutions of the nonlinear biharmonic equation with Dirichlet boundary condition. We give a theorem that there exist at least three nontrivial solutions for the nonlinear biharmonic problem. We prove this result by the finite dimensional reduction method and the shape of the graph of the corresponding functional on the finite reduction subspace.

• Journal of the Chungcheong Mathematical Society
• /
• v.27 no.4
• /
• pp.707-720
• /
• 2014

We get a theorem which shows the existence of at least three solutions for some elliptic system with Dirichlet boundary condition. We obtain this result by using the finite dimensional reduction method which reduces the infinite dimensional problem to the finite dimensional one. We also use the critical point theory on the reduced finite dimensioal subspace.

• Bulletin of the Korean Mathematical Society
• /
• v.27 no.2
• /
• pp.183-188
• /
• 1990

The notion of a Dirichlet set has been studied for several decades. Such sets are named in honour of Dirichlet's Theorem [4, pp.235] which, in modern terminology, simply says that every finite set in R is a dirichlet set. In this paper, we present a structure theorem which characterizes all D-sets on the real line. We also use our structure theorem to give a new proof of a known criterion for proving that a set fails to be a D-set.

• Korean Journal of Mathematics
• /
• v.17 no.2
• /
• pp.211-218
• /
• 2009

We investigate the multiple solutions for a suspending beam equation with jumping nonlinearity crossing three eigenvalues, with Dirichlet boundary condition and periodic condition. We show the existence of at least six nontrivial periodic solutions for the equation by using the finite dimensional reduction method and the geometry of the mapping.