СИБИРСКИЙ МАТЕМАТИЧЕСКИЙ ЖУРНАЛ
SIBIRSKII MATEMATICHESKII ZHURNAL

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 Том 44 (2003), Номер 4, с. 749-771 Копылов А. П. О Wlq-регулярности решений систем дифференциальных уравнений в случае, когда уравнения строятся на основе разрывных функций Получено в определенном отношении окончательное решение проблемы регулярности с точки зрения теории пространств Соболева решений системы (вообще говоря) нелинейных дифференциальных уравнений с частными производными в случае, когда эта система локально близка к эллиптическим системам линейных уравнений с постоянными коэффициентами. Kopylov A. P. On the Wlq-regularity of solutions to systems of differential equations in the case when the equations are constructed from discontinuous functions Some solution, final in a sense from the standpoint of the theory of Sobolev spaces, is obtained to the problem of regularity of solutions to a system of (generally) nonlinear partial differential equations in the case when the system is locally close to elliptic systems of linear equations with constant coefficients. The main consequences of this result are Theorems 5 and 8. According to the first of them, the higher derivatives of an elliptic Cl-smooth solution to a system of lth-order nonlinear partial differential equations constructed from Cl-smooth functions meet the local Hoelder condition with every exponent α, 0<α<1. Theorem 8 claims that if a system of linear partial differential equations of order l with measurable coefficients and right-hand sides is uniformly elliptic then, under the hypothesis of a (sufficiently) slow variation of its leading coefficients, the degree of local integrability of lth-order partial derivatives of every Wlq,loc-solution, q>1, to the system coincides with the degree of local integrability of lower coefficients and right-hand sides. Полный текст статьи / Full texts: PDF file (647 KB) PostScript file (1,2 MB) Адрес редакции: пр. Коптюга, 4, Новосибирск 630090. Телефон: (383-2) 333-493 E-mail: