Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
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Publication:1767870
DOI10.1016/j.camwa.2004.06.006zbMath1155.31303OpenAlexW2021585545MaRDI QIDQ1767870
Publication date: 8 March 2005
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.camwa.2004.06.006
Fundamental solutions to PDEs (35A08) Nonlinear elliptic equations (35J60) Inequalities for sums, series and integrals (26D15) Potential theory on Riemannian manifolds and other spaces (31C12)
Related Items (35)
Embedding theorems for composition of homotopy and projection operators ⋮ Higher integrability of Green's operator and homotopy operator ⋮ Higher integrability of iterated operators on differential forms ⋮ Green’s Operator and Differential Forms ⋮ Singular integrals of the compositions of Laplace-Beltrami and Green's operators ⋮ Inequalities for Green's operator applied to the minimizers ⋮ The existence of solutions to the nonhomogeneous \(\mathcal A\)-harmonic equation ⋮ A new weight class and Poincaré inequalities with the Radon measure ⋮ \(A_r^{\lambda_3}(\lambda_1,\lambda_2,\Omega )\)-weighted inequalities with Lipschitz and BMO norms ⋮ Global estimates for singular integrals of the composite operator ⋮ Imbedding Inequalities for Composition of Green’s and Potential Operators ⋮ Poincaré-type inequalities with \(L^p(\log L)^\alpha\)-norms for Green's operator ⋮ \(L^{\varphi}\)-embedding inequalities for some operators on differential forms ⋮ Lipschitz and BMO norm inequalities for operators ⋮ Norm Inequalities for Singular Integrals Related to Operators and Dirac-Harmonic Equations ⋮ Imbedding theorems in Orlicz-Sobolev space of differential forms ⋮ Recent advances in \(L^p\)-theory of homotopy operator on differential forms ⋮ Poincaré inequalities for composition operators with \(L^\varphi -\)norm ⋮ Norm estimates for the composite operators ⋮ Two-weight Poincaré-type inequalities for differential forms in \(L^s(\mu )\)-averaging domains ⋮ Advances in study of Poincaré inequalities and related operators ⋮ Imbedding inequalities with \(L{\varphi}\)-norms for composite operators ⋮ Poincaré inequalities with Luxemburg norms in \(L^{\varphi}(m)\)-averaging domains ⋮ Poincaré-type inequalities for the homotopy operator with \(L^{\varphi }(\varOmega )\)-norms ⋮ Norms of the composition of the maximal and projection operators ⋮ \(L(\varphi ,\mu )\)-averaging domains and Poincaré inequalities with Orlicz norms ⋮ Hardy-Littlewood and Caccioppoli-type inequalities for \(A\)-harmonic tensors ⋮ Weighted decomposition estimates for differential forms ⋮ Norm inequalities for composition of the Dirac and Green's operators ⋮ Inequalities for Green's operator with Lipschitz and BMO norms ⋮ Poincaré inequalities with the Radon measure for differential forms ⋮ Integral Estimates for the Composition of Green’s and Bounded Operators ⋮ Norm comparison inequalities for the composite operator ⋮ Weak and strong type estimates for multilinear Calderón-Zygmund operators on differential forms ⋮ Dirac-harmonic equations for differential forms
Cites Work
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- Advances in differential forms and the \(A\)-harmonic equation
- Uniform domains and the quasi-hyperbolic metric
- Hardy-Littlewood theorems for \(A\)-harmonic tensors
- Integral estimates for null Lagrangians
- Hardy-Littlewood inequality for quasiregular mappings in certain domains in R^n
- L p Theory of Differential Forms on Manifolds
- On weakly A-harmonic tensors
- Weighted imbedding theorems in the space of differential forms
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