Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms

DOI10.1016/J.NA.2011.03.018zbMath1234.35009OpenAlexW2054715308MaRDI QIDQ540259

Shusen Ding, Jian-Min Zhu

Publication date: 1 June 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2011.03.018

zbMATH Keywords

differential formsOrlicz spacePoincaré inequalityaveraging domains\(A\)-harmonic equation

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Differential forms in global analysis (58A10) Quasilinear elliptic equations (35J62) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items (9)

Estimates for the composition of the Carathéodory and homotopy operators ⋮ Inequalities for integral operators in Hölder-Morrey spaces on differential forms ⋮ Poincaré inequalities and the sharp maximal inequalities with \(L^{\varphi}\)-norms for differential forms ⋮ Recent advances in \(L^p\)-theory of homotopy operator on differential forms ⋮ Estimates for \(L^\varphi \)-Lipschitz and \(L^\varphi \)-BMO norms of differential forms ⋮ Boundedness characterization of composite operator with Orlicz-Lipschitz norm and Orlicz-BMO norm ⋮ Weak and strong type estimates for multilinear Calderón-Zygmund operators on differential forms ⋮ Zeros for the gradients of weakly \(A\)-harmonic tensors ⋮ Higher integrability for very weak solutions of inhomogeneous \(A\)-harmonic form equations

Cites Work

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• \(A_{r}^{\lambda}(\Omega)\)-weighted imbedding inequalities for \(A\)-harmonic tensors.
• Two-weight Poincaré-type inequalities for differential forms in \(L^s(\mu )\)-averaging domains
• Weighted Poincaré-type estimates for conjugate \(A\)-harmonic tensors
• Inequalities for Differential Forms
• General Relativity for Mathematicians
• Approximate Feedback Linearization: A Homotopy Operator Approach
• Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds

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