25 citations · 34 across the 11 of their papers we have counts for
11 papers
Carleman inequalities and unique continuation for the polyharmonic operators
Eunhee Jeong, Yehyun Kwon, Sanghyuk Lee
We obtain a complete characterization of Carleman estimates with weight for the polyharmonic operators. Our result extends the Carleman inequalities for th…
Pointwise convergence for the elastic wave equation
Chu-Hee Cho, Seongyeon Kim, Yehyun Kwon +1
We study pointwise convergence of the solution to the elastic wave equation to the initial data which lies in the Sobolev spaces. We prove that the solution converges along every l…
Quantum revivals and fractality for the Schrödinger equation
Gunwoo Cho, Jimyeong Kim, Seongyeon Kim +2
We investigate the behavior of the Schrödinger equation under the influence of potentials, focusing on its relationship to quantum revivals and fractality. Our findings reveal that…
Strichartz and uniform Sobolev inequalities for the elastic wave equation
Seongyeon Kim, Yehyun Kwon, Sanghyuk Lee +1
We prove dispersive estimate for the elastic wave equation by which we extend the known Strichartz estimates for the classical wave equation to those for the elastic wave equation.…
Strichartz estimates and local regularity for the elastic wave equation with singular potentials
Seongyeon Kim, Yehyun Kwon, Ihyeok Seo
We obtain weighted estimates for the elastic wave equation perturbed by singular potentials including the inverse-square potential. We then deduce the Strichartz estimates un…
Resolvent estimates for the Lamé operator and failure of Carleman estimates
Yehyun Kwon, Sanghyuk Lee, Ihyeok Seo
In this paper, we consider the Lamé operator and study resolvent estimate, uniform Sobolev estimate, and Carleman estimate for . First, we obtain sharp --$L…
Uniqueness in the Calderón problem and bilinear restriction estimates
Seheon Ham, Yehyun Kwon, Sanghyuk Lee
Uniqueness in the Calderón problem in dimension bigger than two was usually studied under the assumption that conductivity has bounded gradient. For conductivities with unbounded g…
Sharp resolvent estimates outside of the uniform boundedness range
Yehyun Kwon, Sanghyuk Lee
In this paper we are concerned with resolvent estimates for the Laplacian in Euclidean spaces. Uniform resolvent estimates for were shown by Kenig, Ruiz and Sogge \cite{KRS…
Carleman estimates and boundedness of associated multiplier operators
Eunhee Jeong, Yehyun Kwon, Sanghyuk Lee
Let be the Laplacian or the wave operator . The following type of Carleman estimate is known to be true on a certain range of : \[ \|e^{v\cdot x}u\|_{L^q(…
Sharp - estimates for the spherical harmonic projection
Yehyun Kwon, Sanghyuk Lee
We consider - estimates for the spherical harmonic projection operators and obtain sharp bounds on a certain range of , . As an application, we provide a proof of o…
Uniform Sobolev inequalities for second order non-elliptic differential operators
Eunhee Jeong, Yehyun Kwon, Sanghyuk Lee
We study uniform Sobolev inequalities for the second order differential operators of non-elliptic type. For we prove that the Sobolev type estimate $\|u\|_{L^q(\math…