arXiv subjects

Woocheol Choi

Publications and source records attributed to Woocheol Choi.

44 records · Page 3Linked to original sources

arXiv2015

On perturbations of the fractional Yamabe problem

The fractional Yamabe problem, proposed by González-Qing (2013, Anal. PDE) is a geometric question which concerns the existence of metrics with constant fractional scalar curvature. It extends the phenomena which were discovered in the classical Yamabe problem and the boundary Yamabe problem to the realm of nonlocal conformally invariant operators. We investigate a non-compactness property of the fractional Yamabe problem by constructing bubbling solutions to its small perturbations.

math.AP↗

arXiv2014

Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents

The objective of this paper is to obtain qualitative characteristics of multi-bubble solutions to the Lane-Emden-Fowler equations with slightly subcritical exponents given any dimension $n \ge 3$. By examining the linearized problem at each $m$-bubble solution, we provide a number of estimates on the first $(n+2)m$-eigenvalues and their corresponding eigenfunctions. Specifically, we present a new proof of the classical theorem due to Bahri-Li-Rey (Calc. Var. Partial Differential Equations 3 (1995) 67-93) which states that if $n \ge 4$, then the Morse index of a multi-bubble solution is governed by a certain symmetric matrix whose component consists of a combination of Green's function, the Robin function, and their first and second derivatives. Our proof also allows us to handle the intricate case $n = 3$.

math.AP↗

arXiv2014

On strongly indefinite systems involving the fractional Laplacian

In this paper we study strongly indefinite systems involving the fractional Laplacian on bounded domains. We obtain existence and non-existence results, $a priori$ estimates of Gidas-Spruck type, and the symmetric property.

math.AP↗

arXiv2014

Asymptotic behavior of solutions for nonlinear elliptic problems with the fractional Laplacian

In this paper we study the asymptotic behavior of least energy solutions and the existence of multiple bubbling solutions of nonlinear elliptic equations involving the fractional Laplacians and the critical exponents. This work can be seen as a nonlocal analog of the results of Han (Ann. Inst. H. Poincare Anal. Non Lineaire, 1991) and Rey (J. Funct. Anal., 1990).

math.AP↗

arXiv2014

Maximal multipliers on compact manifolds without boundary

Hormander-Mihklin type multiplier theorem on compacts manifolds withour boundary has been obtained by using the wave kernels. We consider maximal multiplies on this setting. To obtain the result, we carefully deal with the remainder terms and find an additional information on the wave kernels.

math.AP↗

arXiv2013

L2 and Hp boundedness of strongly singular operators and oscillating operators on Heisenberg groups

In the first part, we obtain sharp results for L^2 boundedness of strongly singular operators on the Heisenberg group. We also define the oscillating convolution operators on the Heisenberg group and study their boundedness properties. In the second part, we obtain the boundedness on Hardy spaces.

math.FA↗

arXiv2013

Maximal multiplier on Stratified groups

In this paper, we prove Lp boundedness of maximal multipliers on stratified groups and maximal multipliers on product spaces of those groups.

math.AP↗

arXiv2012

Oscillating convolution operators on the Heisenberg group

In this paper, we consider oscillating convolution operotors on the Heisenberg group $H^n_a$ with respect to the norm $ρ(x,t) = ρ_1(b x, b t)$ with $ρ_1(x,t)= (|x|^4 + t^2)^{1/4}$. We obtain $L^2$ boundedness properties using the oscillatory integral estimates for degenerate phases in the Euclidean setting. Our result contains an improvement of the Lyall's result for the cases $\frac{a^2}{b^2} \geq C_β$.

math.FA↗