A semihomogeneous elliptic problem with additional unknown functions in boundary conditions
DOI:
https://doi.org/10.15407/dopovidi2015.07.020Keywords:
a priori estimate for solutions, elliptic boundary-value problem, Hörmander space, Noetherian operator, regularity of solutions, slowly varying functionAbstract
We investigate an elliptic boundary-value problem for a homogeneous differential equation, the problem containing additional unknown functions in the boundary conditions. We prove that the operator corresponding to this problem is bounded and Noetherian in appropriate pairs of inner product Sobolev spaces and Hörmander spaces that form a two-sided refined Sobolev scale. For the latter spaces, the regularity indices are an arbitrary real number and a positive function that varies slowly at infinity in the sense of Karamata. We prove theorems on a priori estimates of generalized solutions to the problem and their regularity.
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