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A frequency localized maximum principle and its applications to time fractional equations with rough coefficients
Jae-Hwan Choi, Junhee Ryu
We establish a frequency localized maximum principle for parabolic second-order partial differential equations with the Caputo time fractional derivative of order $α…
Weighted mixed-norm estimates for fractional parabolic equations with space-time nonlocal operators
Hongjie Dong, Junhee Ryu
We establish weighted mixed-norm estimates for fractional parabolic equations \begin{equation*} \partial_t^αu=Lu-λu+f \text{ in } (0,T)\times\mathbb{R}^d, \end{equation*} with nonl…
-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 …
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…
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…
Nonlocal elliptic and parabolic equations with general stable operators in weighted Sobolev spaces
Hongjie Dong, Junhee Ryu
We study nonlocal elliptic and parabolic equations on open sets in weighted Sobolev spaces, where . The operators we consider are infinitesimal generators of…