On L_p-estimates for elliptic and parabolic equations with A_p weights

2016/03/25 by Hongjie Dong, Dong, Hongjie, Doyoon Kim +1 · 7 citations
Mathematics · #35B45 #35J48 #35K25 #35R05 #42B37 #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.1603.07844

openalex publication_date 2016/03/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We prove generalized Fefferman-Stein type theorems on sharp functions with A_p weights in spaces of homogeneous type with either finite or infinite underlying measure. We then apply these results to establish mixed-norm weighted L_p-estimates for elliptic and parabolic equations/systems with (partially) BMO coefficients in regular or irregular domains.

Citations

• Neumann problem for non-divergence elliptic and parabolic equations with BMO_x coefficients in weighted Sobolev spaces
• Hp spaces of several variables

Cited by

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• On some divergence-form singular elliptic equations with codimension-two boundary: L^p-estimates
• Singular-degenerate parabolic systems with the conormal boundary condition on the upper half space
• On nondivergence form linear parabolic and elliptic equations with degenerate coefficients
• Functional calculus on weighted Sobolev spaces for the Laplacian on rough domains

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