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arXiv · 2509.02286

On nondivergence form linear parabolic and elliptic equations with degenerate coefficients

Hongjie Dong·Junhee Ryu
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Abstract

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 nondivergence form, with the leading coefficients given by $x_d^2a_{ij}$, where $a_{ij}$ is bounded, uniformly nondegenerate, and measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. In the remaining spatial variables, they have weighted small mean oscillations. In addition, we investigate the optimality of the function spaces associated with our results.

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Hongjie Dong, Junhee Ryu. 2025-09-02. On nondivergence form linear parabolic and elliptic equations with degenerate coefficients. https://arxiv.org/abs/2509.02286

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