Traces of Generalized Solutions of Elliptic Differential-Difference Equations with Degeneration

This paper is devoted to differential-difference equations with degeneration in a bounded domain Q ⊂ ℝn. We consider differential-difference operators that cannot be expressed as a composition of a strongly elliptic differential operator and a degenerated difference operator. Instead of this, the operators under consideration contain several degenerate difference operators corresponding to differential operators. Generalized solutions of such equations may not belong even to the Sobolev space W21(Q). Earlier, under certain conditions on the difference and differential operators, we obtained a priori estimates and proved that, instead of the whole domain, the orthogonal projection of the generalized solution to the image of the difference operator preserves certain smoothness inside some subdomains Qr⊂Q(UrQ¯r=Q¯). In this paper, we prove necessary and sufficient conditions in algebraic form for the existence of traces on parts of boundaries of subdomains Qr. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Authors
Publisher
Springer New York LLC
Number of issue
6
Language
English
Pages
840-854
Status
Published
Volume
239
Year
2019
Organizations
  • 1 RUDN University, Moscow, Russian Federation
Date of creation
19.07.2019
Date of change
19.07.2019
Short link
https://repository.rudn.ru/en/records/article/record/38558/