Weighted Poincaré inequalities for solutions to \(A\)-harmonic equations.

zbMath1071.35520MaRDI QIDQ1850238

Craig A. Nolder, Shusen Ding

Publication date: 1 January 2003

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Mathematics Subject Classification ID

Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Harmonic, subharmonic, superharmonic functions in higher dimensions (31B05) Differential forms in global analysis (58A10)

Related Items (23)

Orlicz Norm Inequalities for Conjugate Harmonic Forms ⋮ Local and global norm comparison theorems for solutions to the nonhomogeneous A-harmonic equation ⋮ Green’s Operator and Differential Forms ⋮ Advances in differential forms and the \(A\)-harmonic equation ⋮ \(A_r^{\lambda_3}(\lambda_1,\lambda_2,\Omega )\)-weighted inequalities with Lipschitz and BMO norms ⋮ Inequalities for commutators of fractional integrals and singular integrals on differential forms ⋮ Lipschitz and BMO norm inequalities for operators ⋮ Existence of solutions for nonhomogeneous \(A\)-harmonic equations with variable growth ⋮ The existence of solutions to the nonhomogeneous \(A\)-harmonic equations with variable exponent ⋮ Poincaré inequalities for composition operators with \(L^\varphi -\)norm ⋮ Integral estimates for the Laplace-Beltrami and Green's operators applied to differential forms on manifolds ⋮ Sobolev-Poincaré embeddings for operators on harmonic forms on manifolds ⋮ Advances in study of Poincaré inequalities and related operators ⋮ Poincaré inequalities with Luxemburg norms in \(L^{\varphi}(m)\)-averaging domains ⋮ Global estimates for compositions of operators applied to differential forms ⋮ Inequalities for Green's operator with Lipschitz and BMO norms ⋮ Poincaré inequalities with the Radon measure for differential forms ⋮ \(A_{r}(\Omega)\)-weighted inequalities for \(A\)-harmonic tensors and related operators ⋮ Weighted norm inequalities for solutions to the nonhomogeneous \(A\)-harmonic equation ⋮ BMO and Lipschitz norm estimates for composite operators ⋮ The Poincaré lemma, antiexact forms, and fermionic quantum harmonic oscillator ⋮ Zeros for the gradients of weakly \(A\)-harmonic tensors ⋮ Higher integrability for very weak solutions of inhomogeneous \(A\)-harmonic form equations

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