Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.16522 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914088238448640 |
|---|---|
| author | Jung, Pilgyu Woo, Kwan |
| author_facet | Jung, Pilgyu Woo, Kwan |
| contents | We explore the higher integrability of Green's functions associated with the second-order elliptic equation $a^{ij}D_{ij}u + b^i D_iu = f$ in a bounded domain $Ω\subset \mathbb{R}^d$, and establish an enhanced version of Aleksandrov's maximum principle. In particular, we consider the drift term $b=(b^1, \ldots, b^d)$ in $L_d$ and the source term $f \in L_p$ for some $p < d$. This provides an alternative and analytic proof of a result by N. V. Krylov (\textit{Ann. Probab.}, 2021) concerning $L_d$ drifts. The key step involves deriving a Gehring-type inequality for Green's functions by using the Fabes-Stroock approach (\textit{Duke Math. J.}, 1984). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16522 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fabes-Stroock approach to higher integrability of Green's functions and ABP estimates with $L_d$ drift Jung, Pilgyu Woo, Kwan Analysis of PDEs 35B50, 35B45, 35J15 We explore the higher integrability of Green's functions associated with the second-order elliptic equation $a^{ij}D_{ij}u + b^i D_iu = f$ in a bounded domain $Ω\subset \mathbb{R}^d$, and establish an enhanced version of Aleksandrov's maximum principle. In particular, we consider the drift term $b=(b^1, \ldots, b^d)$ in $L_d$ and the source term $f \in L_p$ for some $p < d$. This provides an alternative and analytic proof of a result by N. V. Krylov (\textit{Ann. Probab.}, 2021) concerning $L_d$ drifts. The key step involves deriving a Gehring-type inequality for Green's functions by using the Fabes-Stroock approach (\textit{Duke Math. J.}, 1984). |
| title | Fabes-Stroock approach to higher integrability of Green's functions and ABP estimates with $L_d$ drift |
| topic | Analysis of PDEs 35B50, 35B45, 35J15 |
| url | https://arxiv.org/abs/2408.16522 |