Neumann problem for non-divergence elliptic and parabolic equations with \(\mathrm{BMO}_x\) coefficients in weighted Sobolev spaces

DOI10.3934/dcds.2016011zbMath1351.35039arXiv1502.05594OpenAlexW2963777697MaRDI QIDQ321600

Hongjie Dong, Hong Zhang, Do-Yoon Kim

Publication date: 14 October 2016

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.05594

zbMATH Keywords

weighted Sobolev spacesstochastic partial differential equationselliptic equationsparabolic equations\(\mathrm{BMO}_x\) coefficients\(L_p\) estimatesNeumann boundary value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Initial-boundary value problems for second-order parabolic equations (35K20) PDEs with low regular coefficients and/or low regular data (35R05)

Related Items (3)

Oblique derivative problem for non-divergence parabolic equations with time-discontinuous coefficients in a wedge ⋮ On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights ⋮ Weighted mixed-norm \(L_p\)-estimates for elliptic and parabolic equations in non-divergence form with singular coefficients

Cites Work

• A weighted Sobolev space theory of parabolic stochastic PDEs on non-smooth domains
• \(L_p\) solvability of divergence type parabolic and elliptic systems with partially BMO coefficients
• A weighted \(L_p\)-theory for parabolic PDEs with BMO coefficients on \(C^1\)-domains
• On the \(L_p\)-solvability of higher-order parabolic and elliptic systems with BMO coefficients
• On divergence form SPDEs with VMO coefficients in a half space
• Interior \(W^{2,p}\) estimates for non-divergence elliptic equations with discontinuous coefficients
• A \(W_ 2^ n\)-theory of the Dirichlet problem for SPDEs in general smooth domains
• A weighted \(L_p\)-theory for divergence type parabolic PDEs with BMO coefficients on \(C^1\)-domains
• Solvability of parabolic equations in divergence form with partially BMO coefficients
• Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces
• Parabolic equations with measurable coefficients. II.
• Parabolic equations with VMO coefficients in Sobolev spaces with mixed norms
• Conormal problem of higher-order parabolic systems with time irregular coefficients
• Parabolic equations with variably partially VMO coefficients
• The Dirichlet problem for non-divergence parabolic equations with discontinuous in time coefficients
• Weighted Norm Inequalities for the Hardy-Littlewood Maximal Operator on Spaces of Homogeneous Type
• Parabolic and Elliptic Equations with VMO Coefficients
• W 2,p -Solvability of the Dirichlet Problem for Nondivergence Elliptic Equations with VMO Coefficients
• A Sobolev Space Theory of SPDE with Constant Coefficients on a Half Line
• Weighted sobolev spaces and laplace's equation and the heat equations in a half space
• On The Sobolev Space Theory of Parabolic and Elliptic Equations inC¹Domains
• A Sobolev Space Theory of SPDEs with Constant Coefficients in a Half Space
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