Minsuk Yang

A parabolic Triebel–Lizorkin space estimate for the fractional Laplacian operator

In this paper we prove a parabolic Triebel-Lizorkin space estimate for the operator given by \[T^{\alpha}f(t,x) = \int_0^t \int_{{\mathbb R}^d} P^{\alpha}(t-s,x-y)f(s,y) dyds,\] where the kernel is \[P^{\alpha}(t,x) = \int_{{\mathbb R}^d} e^{2\pi ix\cdot\xi} e^{-t|\xi|^\alpha} d\xi.\] The operator

On convergence of Laplace inversion for the American put option under the CEV model

T^{\alpha}

A new local regularity criterion for suitable weak solutions of the Navier–Stokes equations in terms of the velocity gradient

maps from

An estimate of the second moment of a sampling of the Riemann zeta function on the critical line

L^{p}F_{s}^{p,q}

The Minkowski dimension of interior singular points in the incompressible Navier--Stokes equations

to

Hausdorff Measure of the Singular Set in the Incompressible Magnetohydrodynamic Equations

L^{p}F_{s+\alpha/p}^{p,q}

Local kinetic energy and singularities of the incompressible Navier–Stokes equations

continuously. It has an application to a class of stochastic integro-differential equations of the type

Fundamental solutions for stationary Stokes systems with measurable coefficients

du = -(-\Delta)^{\alpha/2} u dt + f dX_t

Hausdorff measure of boundary singular points in the magnetohydrodynamic equations

.

Existence of suitable weak solutions to the Navier–Stokes equations in time varying domains

In this paper, we study the convergence of the inverse Laplace transform for valuing American put options when the dynamics of the risky asset is governed by the constant elasticity of variance (CEV) model. The CEV model is one popular alternative of the Black-Scholes model to describe well the real financial market. We calculate various coefficients explicitly and prove that the inverse Laplace transform converges absolutely using the properties of Whittaker functions.