Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data

DOI10.1017/S0013091513000758zbMath1325.35075arXiv1210.6566MaRDI QIDQ5173087

Lubomira G. Softova, Vagif S. Guliyev

Publication date: 6 February 2015

Published in: Proceedings of the Edinburgh Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.6566

zbMATH Keywords

BMOsublinear operatorsCauchy-Dirichlet problemVMOgeneralized Morrey spacesCalderón-Zygmund integrals

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Initial-boundary value problems for second-order parabolic equations (35K20) A priori estimates in context of PDEs (35B45) PDEs with low regular coefficients and/or low regular data (35R05) Linear operators on function spaces (general) (47B38) Strong solutions to PDEs (35D35)

Related Items (18)

Gradient estimates in generalized Morrey spaces for parabolic operators ⋮ Anisotropic fractional maximal commutators with BMO functions on anisotropic Morrey-type spaces ⋮ Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces ⋮ Corrigendum to: ``Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces ⋮ Gradient estimates for parabolic equations in generalized weighted Morrey spaces ⋮ Boundedness of the maximal operator and its commutators on vanishing generalized Orlicz-Morrey spaces ⋮ Characterizations for the commutator of parabolic nonsingular integral operator on parabolic generalized Orlicz-Morrey spaces ⋮ Global regularity in Orlicz-Morrey spaces of solutions to parabolic equations with \textit{VMO} coefficients ⋮ Hardy-Littlewood, Bessel-Riesz, and fractional integral operators in anisotropic Morrey and Campanato spaces ⋮ Unnamed Item ⋮ Multilinear commutators of Calderón-Zygmund operator on generalized weighted Morrey spaces ⋮ Parabolic oblique derivative problem with discontinuous coefficients in generalized Morrey spaces ⋮ Fractional multilinear integrals with rough kernels on generalized weighted Morrey spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Global gradient estimates in weighted Lebesgue spaces for parabolic operators ⋮ Gradient estimates of parabolic Cauchy-Dirichlet problems on Morrey-Banach spaces

Cites Work

• Unnamed Item
• Boundedness of sublinear operators and commutators on generalized Morrey spaces
• Parabolic oblique derivative problem with discontinuous coefficients in generalized Morrey spaces
• Morrey-type regularity of solutions to parabolic problems with discontinuous data
• Boundedness of the maximal, potential and singular operators in the generalized Morrey spaces
• On \(BMO\) regularity for linear elliptic systems
• Singular integral operators, Morrey spaces and fine regularity of solutions to PDEs
• Global regularity in generalized Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients
• Singular integral operators in Morrey spaces and interior regularity of solutions to systems of linear PDE's
• Singular integrals and commutators in generalized Morrey spaces
• On functions of bounded mean oscillation
• The Campanato, Morrey and Hölder spaces on spaces of homogeneous type
• W_p^1,2solvability for the cauchy-dirichlet problem for parabolic equations with vmo coefficients
• Hardy-Littlewood Maximal Operator, Singular Integral Operators and the Riesz Potentials on Generalized Morrey Spaces

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