4 papers
A regularity theory for second-order parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces
Jae-Hwan Choi, Junhee Ryu
We develop an optimal regularity theory for parabolic partial differential equations in weighted mixed norm Sobolev-Zygmund spaces. The results extend the classical Schauder estima…
On nondivergence form linear parabolic and elliptic equations with degenerate coefficients
Hongjie Dong, Junhee Ryu
We establish the unique solvability in weighted mixed-norm Sobolev spaces for a class of degenerate parabolic and elliptic equations in the upper half space. The operators are in n…
-estimates for nonlocal equations with general Lévy measures
Hongjie Dong, Junhee Ryu
We consider nonlocal operators of the form \begin{equation*} L_t u(x) = \int_{\mathbb{R}^d} \left( u(x+y)-u(x)-\nabla u(x)\cdot y^{(Ï)} \right) ν_t(dy), \end{equation*} where $ν…
Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients
Hongjie Dong, Junhee Ryu
We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space . The leading coefficients are of the form , wher…