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arXiv · 2412.00779

Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients

Hongjie Dong·Junhee Ryu
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Abstract

We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are bounded, uniformly elliptic, and measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. Additionally, they have small bounded mean oscillations in the other spatial variables. We obtain the well-posedness and regularity of solutions in weighted mixed-norm Sobolev spaces.

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Hongjie Dong, Junhee Ryu. 2024-12-01. Sobolev estimates for parabolic and elliptic equations in divergence form with degenerate coefficients. https://arxiv.org/abs/2412.00779

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