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 Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 5, Pages 35–48 (Mi izv450)

On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations

A. A. Kovalevsky

Abstract: We present some results on the summability of entropy solutions for the Dirichlet problem in a class of fourth-order non-linear elliptic equations in relation to integrability properties of their right-hand sides. Consideration is given to the cases in which the right-hand sides belong to Lebesgue spaces with exponents close to unity and also to some wider sets contained in $L^1$.

DOI: https://doi.org/10.4213/im450

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English version:
Izvestiya: Mathematics, 2003, 67:5, 881–894

Bibliographic databases:

UDC: 517.9
MSC: 35B45, 35D05, 35K60, 35R10

Citation: A. A. Kovalevsky, “On the summability of entropy solutions for the Dirichlet problem in a class of non-linear elliptic fourth-order equations”, Izv. RAN. Ser. Mat., 67:5 (2003), 35–48; Izv. Math., 67:5 (2003), 881–894

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/izv450
• https://doi.org/10.4213/im450
• http://mi.mathnet.ru/eng/izv/v67/i5/p35

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Kovalevsky A.A., Nicolosi F., “On limit summability of solutions for a class of degenerate nonlinear high-order equations with L-1-data”, Complex Variables and Elliptic Equations, 55:11 (2010), 1047–1058
2. A. A. Kovalevsky, Yu. S. Gorban, “On $T$-solutions of degenerate anisotropic elliptic variational inequalities with $L^1$-data”, Izv. Math., 75:1 (2011), 101–156
3. Voitovych M.V., “Pointwise Estimates of Solutions to 2M-Order Quasilinear Elliptic Equations With M- (P, Q) Growth Via Wolff Potentials”, Nonlinear Anal.-Theory Methods Appl., 181 (2019), 147–179
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