×

Weighted decomposition estimates for differential forms. (English) Zbl 1200.46029

Summary: After introducing the definition of \(A_{r,\lambda}^\beta\)-weights, we establish the \(A_r(\Omega)\)-weighted decomposition estimates and \(A_{r,\lambda}^\beta(\Omega)\)-weighted Caccioppoli-type estimates for \(A\)-harmonic tensors. Furthermore, by Whitney’s covering lemma, we obtain the global results in domain \(\Omega\subset \mathbb R^n\). These results can be used to study the integrability of differential forms and to estimate the integrals for differential forms.

MSC:

46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
58A10 Differential forms in global analysis
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Wang Y, Wu C: Global Poincaré inequalities for Green’s operator applied to the solutions of the nonhomogeneous -harmonic equation. Computers & Mathematics with Applications 2004, 47(10-11):1545-1554. 10.1016/j.camwa.2004.06.006 · Zbl 1155.31303 · doi:10.1016/j.camwa.2004.06.006
[2] Ding S: Weighted Caccioppoli-type estimates and weak reverse Hölder inequalities for -harmonic tensors. Proceedings of the American Mathematical Society 1999, 127(9):2657-2664. 10.1090/S0002-9939-99-05285-5 · Zbl 0926.30013 · doi:10.1090/S0002-9939-99-05285-5
[3] Perić I, Žubrinić D: Caccioppoli’s inequality for quasilinear elliptic operators. Mathematical Inequalities and Applications 1999, 2(2):251-261. · Zbl 0924.35044
[4] Nolder CA: Hardy-Littlewood theorems for -harmonic tensors. Illinois Journal of Mathematics 1999, 43(4):613-631. · Zbl 0957.35046
[5] Scott C: theory of differential forms on manifolds. Transactions of the American Mathematical Society 1995, 347(6):2075-2096. 10.2307/2154923 · Zbl 0849.58002 · doi:10.2307/2154923
[6] Gilbarg D, Trudinger NS: Elliptic Partial Differential Equations of Second Order, Grundlehren der Mathematischen Wissenschaften. Volume 224. 2nd edition. Springer, Berlin, Germany; 1983:xiii+513. · Zbl 0361.35003 · doi:10.1007/978-3-642-61798-0
[7] Iwaniec T, Lutoborski A: Integral estimates for null Lagrangians. Archive for Rational Mechanics and Analysis 1993, 125(1):25-79. 10.1007/BF00411477 · Zbl 0793.58002 · doi:10.1007/BF00411477
[8] Garnett JB: Bounded Analytic Functions. Academic Press, New York, NY, USA; 1970.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.