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초록
We explore the higher integrability of Green's functions associated with the second-order elliptic equation aijDiju+biDiu=f in a bounded domain Ω⊂Rd, and establish an enhanced version of Aleksandrov's maximum principle. In particular, we consider the drift term b=(b1,…,bd) in Ld and the source term f∈Lp for some p<d. This provides an alternative and analytic proof of a result by N.V. Krylov (Ann. Probab., 2021) concerning Ld drifts. The key step involves deriving a Gehring-type inequality for Green's functions by using the Fabes-Stroock approach (Duke Math. J., 1984).
키워드
Aleksandrov's maximum principle; Critical drift; Gehring's lemma; Green's function; ELLIPTIC-EQUATIONS; DIRICHLET PROBLEM
- 제목
- Fabes-Stroock approach to higher integrability of Green's functions and ABP estimates with Ld drift
- 저자
- Jung, Pilgyu; Woo, Kwan
- 발행일
- 2025-12
- 유형
- Article
- 권
- 204