In this note we investigate the regularity theory for weak solutions of second-order elliptic partial differential equations whose coefficients belong to the space of functions of bounded mean oscillation (BM O). The main contribution of this work is to establish that weak solutions possess second derivatives in appropriate Lq spaces. Our techniques combine harmonic analysis, variational methods, and delicate perturbation estimates.
A NOTE ON ELLIPTIC EQUATIONS WITH BMO COEFFICIENTS: REGULARITY THEORY
D'Onofrio, Luigi
2026-01-01
Abstract
In this note we investigate the regularity theory for weak solutions of second-order elliptic partial differential equations whose coefficients belong to the space of functions of bounded mean oscillation (BM O). The main contribution of this work is to establish that weak solutions possess second derivatives in appropriate Lq spaces. Our techniques combine harmonic analysis, variational methods, and delicate perturbation estimates.File in questo prodotto:
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