We consider elliptic boundary-value problems in which the elliptic operator is a polynomial function of a small parameter and the boundary conditions contain additional unknown functions. It is shown that the condition of ellipticity with small parameter is not only sufficient but also necessary for the a priori estimation of the solutions to this problem in the corresponding special functional spaces depending on the parameter.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 9, pp. 1269–1275, September, 2014.
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Zavorotinskii, A.V. On Elliptic Boundary-Value Problems with Small Parameter and Additional Functions on the Boundary of a Domain. Ukr Math J 66, 1423–1430 (2015). https://doi.org/10.1007/s11253-015-1021-4
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DOI: https://doi.org/10.1007/s11253-015-1021-4