Elliptic problems with rough boundary data in Nikolskii spaces
Analysis of PDEs
2021-03-19 v1
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, the 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.
Keywords
Cite
@article{arxiv.2103.10372,
title = {Elliptic problems with rough boundary data in Nikolskii spaces},
author = {A. A. Murach and I. S. Chepurukhina},
journal= {arXiv preprint arXiv:2103.10372},
year = {2021}
}
Comments
9 pages. Ukrainian