Elliptic problems with rough boundary data in Nikolskii spaces
DOI:
https://doi.org/10.15407/dopovidi2021.03.003Keywords:
elliptic boundary-value problem, Nikolskii space, Fredholm operator, regularity of solution, a priori estimate, white noiseAbstract
We investigate a general elliptic problem given in a bounded Euclidean domain with boundary data in Nikolskii
spaces of low, specifically, negative order. The right-hand side of the elliptic differential equation is supposed to
be an integrable function. We establish the Fredholm property of the problem, maximal regularity, and a priori
estimate of its generalized solutions in the spaces indicated. We give an application of these results to some
elliptic problems with boundary conditions induced by a Gaussian white noise
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