Higher-order elliptic and parabolic equations with VMO assumptions and general boundary conditions

2017/02/10 by Hongjie Dong, Dong, Hongjie, Chiara Gallarati +1
Mathematics · #35B45 #35K25 #35R05 #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1702.03254

openalex publication_date 2017/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove mixed L_p(L_q)-estimates, with p,q∈(1,∞), for higher-order elliptic and parabolic equations on the half space \R^d+1₊ with general boundary conditions which satisfy the Lopatinskii--Shapiro condition. We assume that the elliptic operators A have leading coefficients which are in the class of vanishing mean oscillations in both the time and the space variable. In the proof, we produce mean oscillation estimates for equations on the half space with general boundary conditions.

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