Second-order elliptic equations with variably partially VMO coefficients

DOI10.1016/j.jfa.2009.06.014zbMath1171.35352arXiv0807.0926OpenAlexW2046718381MaRDI QIDQ841495

Nicolai V. Krylov

Publication date: 17 September 2009

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.0926

zbMATH Keywords

Sobolev spacessecond-order elliptic equationsvanishing mean oscillationpartially VMO coefficients

Mathematics Subject Classification ID

Related Items (47)

Elliptic and parabolic equations with measurable coefficients in weighted Sobolev spaces ⋮ W2,p a priori estimates for nonvariational operators: the sharp maximal function technique ⋮ Parabolic equations with variably partially VMO coefficients ⋮ Global weighted estimates in Orlicz spaces for second-order nondivergence parabolic equations ⋮ Weighted \(W^{1, p}\) estimates for weak solutions of degenerate elliptic equations with coefficients degenerate in one variable ⋮ Morrey regularity of solutions to quasilinear elliptic equations over Reifenberg flat domains ⋮ Global \({L}_p\) estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form ⋮ Regularity estimates for higher order elliptic systems on Reifenberg flat domains ⋮ Uniformly nondegenerate elliptic equations with partially BMO coefficients in nonsmooth domains ⋮ Gradient Estimates for Stokes and Navier--Stokes Systems with Piecewise DMO Coefficients ⋮ On elliptic equations in a half space or in convex wedges with irregular coefficients ⋮ Global gradient estimates for general nonlinear parabolic equations in nonsmooth domains ⋮ Gradient estimates for higher order elliptic equations on nonsmooth domains ⋮ Interior \(W^{2, p(x)}\)-regularity for elliptic equations of nondivergence form ⋮ Elliptic Venttsel problems with \(VMO\) coefficients ⋮ Higher-order nondivergence elliptic and parabolic equations in Sobolev spaces and Orlicz spaces ⋮ Second-order elliptic equations of nondivergence form with small BMO coefficients in \(\mathbb R^{n }\) ⋮ Global weighted regularity estimates for higher‐order elliptic and parabolic systems ⋮ \(L_p\) solvability of divergence type parabolic and elliptic systems with partially BMO coefficients ⋮ Orlicz estimates for nondivergence linear elliptic equations with partially BMO coefficients ⋮ Higher order elliptic and parabolic systems with variably partially BMO coefficients in regular and irregular domains ⋮ Elliptic equations with measurable coefficients in Reifenberg domains ⋮ Global regularity for higher order divergence elliptic and parabolic equations ⋮ High order Fefferman-Phong type inequalities in Carnot groups and regularity for degenerate elliptic operators plus a potential ⋮ Solvability of second-order equations with hierarchically partially BMO coefficients ⋮ On $L_p$-estimates for elliptic and parabolic equations with $A_p$ weights ⋮ The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition ⋮ Weighted \(L_{q}\)-estimates for stationary Stokes system with partially BMO coefficients ⋮ Weighted Lorentz estimates for nondivergence linear elliptic equations with partially BMO coefficients ⋮ Global weighted estimates for second-order nondivergence elliptic and parabolic equations ⋮ Solvability of parabolic equations in divergence form with partially BMO coefficients ⋮ Elliptic equations in divergence form with partially BMO coefficients ⋮ On the \(L_p\)-solvability of higher-order parabolic and elliptic systems with BMO coefficients ⋮ Gradient estimates for elliptic systems with measurable coefficients in nonsmooth domains ⋮ Regularity in Orlicz spaces for non-divergence degenerate elliptic equations on homogeneous groups ⋮ Second-order elliptic and parabolic equations with $B(\mathbb{R}^{2}, VMO)$ coefficients ⋮ Regularity in Orlicz spaces for nondivergence degenerate elliptic equations in Carnot groups ⋮ Second-order elliptic and parabolic equations with BMO coefficients in the whole space ⋮ Venttsel Boundary Value Problems with Discontinuous Data ⋮ On stochastic equations with drift in \({L_d}\) ⋮ Unnamed Item ⋮ Rubio de Francia extrapolation theorem and related topics in the theory of elliptic and parabolic equations. A survey ⋮ Unnamed Item ⋮ Lq-Estimates for stationary Stokes system with coefficients measurable in one direction ⋮ Unnamed Item ⋮ Another approach of Morrey estimate for linear elliptic equations with partially BMO coefficients in a half space ⋮ Elliptic Obstacle Problems with Measurable Coefficients in Non-Smooth Domains

Cites Work

• Parabolic and elliptic systems with VMO coefficients
• Elliptic and parabolic equations with measurable coefficients in \(L_p\)-spaces with mixed norms
• Interior \(W^{2,p}\) estimates for non-divergence elliptic equations with discontinuous coefficients
• Elliptic Differential Equations with Coefficients Measurable with Respect to One Variable and VMO with Respect to the Others
• $L^p$ estimates for general nonlinear elliptic equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II
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