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math.AP2025
-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^{(σ)} \right) ν_t(dy), \end{equation*} where …
math.AP2025
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…
math.AP2025
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…