Generalized Morrey regularity for parabolic equations with discontinuity data

2012/10/24 by Vagif S. Guliyev, Guliyev, Vagif S., Lubomira G. Softova +1
Computer Science · Mathematics · #35K15 #42B20 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · doi:10.48550/arxiv.1210.6566

openalex publication_date 2012/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We obtain continuity in generalized parabolic Morrey spaces of sublinear integrals generated by the parabolic Calderón-Zygmund operators and its commutator with VMO functions. The obtained estimates are used to study global regularity of the solutions of the Cauchy-Dirichlet problem for linear uniformly parabolic equations with discontinuous coefficients.

Citations

• On functions of bounded mean oscillation
• On the solutions of quasi-linear elliptic partial differential equations

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