Elliptic problems with rough boundary data in Nikolskii spaces

2021/03/18 by Murach, A. A., Chepurukhina, I. S.
#35J40 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2103.10372

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.

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