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Algebra i Analiz, 2019, Volume 31, Issue 3, Pages 10–35 (Mi aa1650)  
This article is cited in 12 scientific papers (total in 12 papers)

Expository Surveys

Survey on gradient estimates for nonlinear elliptic equations in various function spaces

S.-S. Byuna, D. K. Palagachevb, L. G. Softovac

a Department of Mathematics and Research Institute of Mathematics, Seoul National University, Seoul 151-747, Korea
b Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy
c Department of Mathematics, University of Salerno, 84084 Fisciano, Italy
Full-text PDF (317 kB) Citations (12)
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Abstract: Very general nonvariational elliptic equations of $ p$-Laplacian type are treated. An optimal Calderón-Zygmund theory is developed for such a nonlinear elliptic equation in divergence form in the setting of various function spaces including Lebesgue spaces, Orlicz spaces, weighted Orlicz spaces, and variable exponent Lebesgue spaces. The addressed arguments also apply to Morrey spaces, Lorentz spaces and generalized Orlicz spaces.
Keywords: gradient estimate, nonlinear elliptic equation, $L^p$ space, weighted Lebesgue space, Orlicz space, BMO, Muckenhoupt weight, Reifenberg flat domain.
Funding agency Grant number
National Research Foundation of Korea NRF-2015R1A4A1041675
Istituto Nazionale di Alta Matematica "Francesco Severi"
S.-S. Byun was supported by NRF-2015R1A4A1041675. D. K. Palagachev and L. G. Softova are members of INdAM/GNAMPA
Received: 08.10.2018
English version:
St. Petersburg Mathematical Journal, 2020, Volume 31, Issue 3, Pages 401–419
DOI: https://doi.org/10.1090/spmj/1605
Bibliographic databases:
Document Type: Article
MSC: Primary 35J60, 35R05; Secondary 35B65, 46E30, 46E35
Language: English
Citation: S.-S. Byun, D. K. Palagachev, L. G. Softova, “Survey on gradient estimates for nonlinear elliptic equations in various function spaces”, Algebra i Analiz, 31:3 (2019), 10–35; St. Petersburg Math. J., 31:3 (2020), 401–419
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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