Elliptic problems with rough boundary data in Nikolskii spaces

Authors

DOI:

https://doi.org/10.15407/dopovidi2021.03.003

Keywords:

elliptic boundary-value problem, Nikolskii space, Fredholm operator, regularity of solution, a priori estimate, white noise

Abstract

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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Published

06.07.2021

How to Cite

Murach О., & Chepurukhina І. (2021). Elliptic problems with rough boundary data in Nikolskii spaces. Reports of the National Academy of Sciences of Ukraine, (3), 3–10. https://doi.org/10.15407/dopovidi2021.03.003