We consider a linear elliptic system of second order equations with constant coefficients in a neighborhood of the plane part of the boundary. The boundary condition contains the conormal derivative and the second order operator containing the tangent derivatives (a Venttsel type problem). For a weak solution we obtain the fundamental Campanato estimates. We clarify the dependence of the smoothness of a weak solution to the corresponding inhomogeneous problem in Campanato spaces on the smoothness of the right-hand sides of the system and boundary conditions. Bibliography: 8 titles.
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Translated from Problemy Matematicheskogo Analiza 70, May 2013, pp. 47–56.
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Arkhipova, A.A., Lukina, A.A. Estimates for solutions to the model Venttsel problem in Campanato spaces. J Math Sci 191, 150–161 (2013). https://doi.org/10.1007/s10958-013-1309-6
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DOI: https://doi.org/10.1007/s10958-013-1309-6