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Эта публикация цитируется в 11 научных статьях (всего в 11 статьях)
Обзоры
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
Аннотация:
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.
Ключевые слова:
gradient estimate, nonlinear elliptic equation, $L^{p}$ space, weighted Lebesgue space, Orlicz space, BMO, Muckenhoupt weight, Reifenberg flat domain.
Поступила в редакцию: 08.10.2018
Образец цитирования:
S.-S. Byun, D. K. Palagachev, L. G. Softova, “Survey on gradient estimates for nonlinear elliptic equations in various function spaces”, Алгебра и анализ, 31:3 (2019), 10–35; St. Petersburg Math. J., 31:3 (2020), 401–419
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/aa1650 https://www.mathnet.ru/rus/aa/v31/i3/p10
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