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Regularity results for quasilinear elliptic systems with nonlinear boundary conditions

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Abstract

It is proved that a solution of the boundary-value problem for a second-order quasilinear system with controlled order of nonlinearity is partially smooth all the way to the boundary of a domain. The boundary condition is imposed by means of a second-order nonlinear operator which can be regarded as a generalization of the “directional derivative” to the case of quasilinear systems. Bibliography: 6 titles.

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Literature Cited

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Authors
  1. A. A. Arkhipova
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Additional information

Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995, pp. 23–50.

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Arkhipova, A.A. Regularity results for quasilinear elliptic systems with nonlinear boundary conditions. J Math Sci 77, 3277–3294 (1995). https://doi.org/10.1007/BF02364861

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  • DOI: https://doi.org/10.1007/BF02364861

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