Global integrability theorems for \(A\)-harmonic tensors

DOI10.1006/jmaa.2000.6850zbMath0973.35074OpenAlexW1978705867MaRDI QIDQ1576978

Craig A. Nolder

Publication date: 27 November 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6850

zbMATH Keywords

BMOglobal integrability of gradientsWhitney cube number condition

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Other generalizations (nonlinear potential theory, etc.) (31C45)

Related Items (18)

Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds ⋮ Orlicz norm inequalities for the composite operator and applications ⋮ Carathéodory operator of differential forms ⋮ The existence of solutions to the nonhomogeneous \(\mathcal A\)-harmonic equation ⋮ Advances in differential forms and the \(A\)-harmonic equation ⋮ Estimates for the composition of the Carathéodory and homotopy operators ⋮ Weighted integral inequalities for conjugate \(A\)-harmonic tensors. ⋮ Some local Poincaré inequalities for the composition of the sharp maximal operator and the Green's operator ⋮ Poincaré-type inequalities with \(L^p(\log L)^\alpha\)-norms for Green's operator ⋮ Nonlinear \(A\)-Dirac equations ⋮ Poincaré inequalities for composition operators with \(L^\varphi -\)norm ⋮ Some strong \((p,q)\)-type inequalities for the homotopy operator ⋮ Some new integral inequalities for conjugate \(A\)-harmonic tensors ⋮ Norms of the composition of the maximal and projection operators ⋮ Some priori estimates about solutions to nonhomogeneous \(A\)-harmonic equations ⋮ Global estimates for singular integrals of the composition of the maximal operator and the Green's operator ⋮ Some estimates of integrals with a composition operator ⋮ A singular integral of the composite operator

Cites Work

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• Whitney cubes, p-capacity, and Minkowski content
• Hardy-Littlewood theorems for \(A\)-harmonic tensors
• Integral estimates for null Lagrangians
• Quasiconformal mappings and global integrability of the derivative
• \(p\)-harmonic tensors and quasiregular mappings
• The radial variation of analytic functions
• L^p-averaging domains and the Poincaré inequality
• Lipschitz classes and quasiconformla mappings
• The Degree of Regularity of a Quasiconformal Mapping
• Global integrability of the gradients of solutions to partial differential equations
• On weakly A-harmonic tensors
• Mean Oscillation Over Cubes and Holder Continuity

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