\(L ^{p }\)-regularity for fourth order parabolic systems with measurable coefficients

DOI10.1007/s00209-011-0947-yzbMath1255.35132OpenAlexW1996753681MaRDI QIDQ455627

Sun-Sig Byun, Lihe Wang

Publication date: 22 October 2012

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00209-011-0947-y

zbMATH Keywords

BMO spaceHessian estimateinear laminate

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) PDEs with low regular coefficients and/or low regular data (35R05) Second-order parabolic systems (35K40) Higher-order parabolic systems (35K41)

Related Items (5)

Gradient estimates in generalized Morrey spaces for parabolic operators ⋮ \(L_p\)-estimates for time fractional parabolic equations in divergence form with measurable coefficients ⋮ Global gradient estimates in weighted Lebesgue spaces for parabolic operators ⋮ Hessian estimates for fourth order elliptic systems with singular BMO coefficients in composite Reifenberg domains ⋮ Generalized Morrey estimates for the gradient of divergence form parabolic operators with discontinuous coefficients

Cites Work

• Gradient continuity estimates
• Gradient estimates for a class of parabolic systems
• Fourth-order parabolic equations with weak BMO coefficients in Reifenberg domains
• Parabolic equations with partially BMO coefficients and boundary value problems in Sobolev spaces with mixed norms
• Hessian estimates in Orlicz spaces for fourth-order parabolic systems in non-smooth domains
• A geometric approach to the Calderón-Zygmund estimates
• Smoothness of linear laminates
• Elliptic equations with measurable coefficients in Reifenberg domains
• Higher integrability for parabolic systems of \(p\)-Laplacian type
• Self-improving property of nonlinear higher order parabolic systems near the boundary
• Solvability of parabolic equations in divergence form with partially BMO coefficients
• Second-order elliptic and parabolic equations with $B(\mathbb{R}^{2}, VMO)$ coefficients
• On functions of bounded mean oscillation
• Parabolic and Elliptic Equations with VMO Coefficients
• Quasilinear divergence form elliptic equations in rough domains
• Functions of Vanishing Mean Oscillation
• Estimates for elliptic systems from composite material
• Gradient estimates for thep(x)-Laplacean system
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