Morrey-type regularity of solutions to parabolic problems with discontinuous data

DOI10.1007/s00229-011-0447-8zbMath1270.35153OpenAlexW2076175174MaRDI QIDQ644993

Lubomira G. Softova

Publication date: 8 November 2011

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-011-0447-8

zbMATH Keywords

Dirichlet problemregular oblique derivative problemnon-divergence typeVMO principal coefficients

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) 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) Strong solutions to PDEs (35D35)

Related Items (18)

Estimates for operators on generalized weighted Orlicz-Morrey spaces and their applications to non-divergence elliptic equations ⋮ Gradient estimates in generalized Morrey spaces for parabolic operators ⋮ Approximation in generalized Morrey spaces ⋮ Parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces ⋮ Gradient estimates for parabolic equations in generalized weighted Morrey spaces ⋮ Weighted Orlicz estimates for general nonlinear parabolic equations over nonsmooth domains ⋮ Global regularity in generalized Morrey spaces of solutions to nondivergence elliptic equations with VMO coefficients ⋮ Global regularity in Orlicz-Morrey spaces of solutions to parabolic equations with \textit{VMO} coefficients ⋮ Parabolic oblique derivative problem with discontinuous coefficients in generalized Morrey spaces ⋮ Maximal commutators and commutators of potential operators in new vanishing Morrey spaces ⋮ The Dirichlet Problem for Elliptic Equations with VMO Coefficients in Generalized Morrey Spaces ⋮ Generalized Morrey Regularity for Parabolic Equations with Discontinuous Data ⋮ Global gradient estimates in weighted Lebesgue spaces for parabolic operators ⋮ Some estimates for the commutators of multilinear maximal function on Morrey-type space ⋮ On the invariance of certain vanishing subspaces of Morrey spaces with respect to some classical operators ⋮ Gradient estimates of parabolic Cauchy-Dirichlet problems on Morrey-Banach spaces ⋮ Boundedness of Bilinear Fractional Integral Operators on Vanishing Generalized Morrey Spaces ⋮ Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients

Cites Work

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• Gradient potential estimates
• Gradient estimates below the duality exponent
• Interior \(W^{2,p}\) estimates for non-divergence elliptic equations with discontinuous coefficients
• Oblique derivative problem for parabolic operators with VMO coefficients
• Singular integrals and commutators in generalized Morrey spaces
• On the existence of certain singular integrals
• Singular Integral Operators and Differential Equations
• On functions of bounded mean oscillation
• W 2,p -Solvability of the Dirichlet Problem for Nondivergence Elliptic Equations with VMO Coefficients
• Functions of Vanishing Mean Oscillation
• 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
• Singular integrals with mixed homogeneity

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