| Luigi D’Onofrio†
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 (BMO). 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. Keywords: elliptic partial differential equations, BMO coefficients, regularity theory, good-λ inequality, second derivative estimates. MSC: 35J15, 35J25, 35B65, 42B35, 35D30. DOI 10.56082/annalsarscimath.2026.1.117 †luigi.donofrio@uniparthenope.it, Dipartimento di Scienze e Tecnologie, Università degli Studi di Napoli Parthenope, Centro Direzionale, Isola C4, 80143 Napoli, Italy |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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