On regularity of solutions to systems of partial differential equations which are locally close to elliptic systems of linear equations with constant coefficients. II.(English. Russian original)Zbl 0951.35037

Sib. Math. J. 41, No. 1, 81-99 (2000); translation from Sib. Mat. Zh. 41, No. 1, 98-117 (2000).
The article under review is a concluding part of the preceding article by the author see [Sib. Math. J. 40, No. 4, 726-741 (1999; Zbl 0935.35022)] which is devoted to the study of the local $$W^l_q$$-regularity of solutions to elliptic systems locally close to elliptic systems with constant coefficients. The author proves an auxiliary theorem that was used in the preceding article and discusses similar assertions. He also presents a final precise statement of the main result on the local regularity of solutions.

MSC:

 35J45 Systems of elliptic equations, general (MSC2000) 35B65 Smoothness and regularity of solutions to PDEs 35J60 Nonlinear elliptic equations

Zbl 0935.35022
Full Text:

References:

 [1] Kopylov A. P., ”On regularity of solutions to systems of partial differential equations which are locally close to elliptic systems of linear equations with constant coefficients. I,” Sibirsk. Mat. Zh.,40, No. 4, 861–879 (1999). · Zbl 0935.35022 [2] Sobolev S. L., Some Applications of Functional Analysis to Mathematical Physics [in Russian], Izdat. Sibirsk. Otdel. Akad. Nauk SSSR, Novosibirsk (1962). · Zbl 0126.31804 [3] Kopylov A. P., Stability in theC-Norm of Classes of Mappings [in Russian], Nauka, Novosibirsk (1990). · Zbl 0772.30023 [4] Stein E. M., Singular Integrals and Differentiability Properties of Functions [Russian translation], Mir, Moscow (1973). [5] Kopylov A. P., ”Stability in theC l-norm of classes of solutions to systems of linear partial differential equations of elliptic type,” Sibirsk. Mat. Zh.,40, No. 2, 352–371 (1999). · Zbl 0947.30013 [6] Kopylov A. P. ”OnWq/l-regularity of solutions to systems of partial differential equations which are locally close to elliptic systems of linear equations with constant coefficients,” Dokl. Akad. Nauk,368, No. 3, 303–306 (1999). · Zbl 1071.35510
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.