3 citations · 11 across the 18 of their papers we have counts for
18 papers
Hölder regularity of weak solutions to nonlocal -Laplacian type Schrödinger equations with -Muckenhoupt potentials
Yong-Cheol Kim
In this paper, using the De Giorgi-Nash-Moser method, we obtain an interior Hölder continuity of weak solutions to nonlocal -Laplacian type Schrödinger equations given by an int…
Nonlocal Harnack inequalities for nonlocal heat equations
Yong-Cheol Kim
In this paper, applying the De Giorgi method, we obtain nonlocal Harnack inequalities for weak solutions of nonlocal parabolic equations given by an integro-differential operator $…
mapping properties for nonlocal Schrödinger operators with certain potential
Woocheol Choi, Yong-Cheol Kim
In this paper, we consider nonlocal Schrödinger equations with certain potentials given by an integro-differential operator as follows; \begin{equation*}L_K u+V u=f\,\,\t…
The Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with certain potentials
Woocheol Choi, Yong-Cheol Kim
In this paper, we prove the Malgrange-Ehrenpreis theorem for nonlocal Schrödinger operators with nonnegative potentials $V\in L^q_{\loc}(\BR^n)$ for $q>\f{n}{2s}$ with $0<s…
A refinement of the Berezin-Li-Yau type inequality for nonlocal elliptic operators
Yong-Cheol Kim
In this paper, we prove a refinement of the Berezin-Li-Yau type inequality for a wider class of nonlocal elliptic operators including the fractional Laplacians $-(-Δ^{\sm/2})$ rest…
Regularity for fully nonlinear integro-differential operators with regularly varying kernels
Soojung Kim, Yong-Cheol Kim, Ki-Ahm Lee
In this paper, the regularity results for the integro-differential operators of the fractional Laplacian type by Caffarelli and Silvestre \cite{CS1} are extended to those for the i…