On some distributions associated to boundary value problems

Abstract

We consider an elliptic pseudo-differential equation in a multidimensional cone in Sobolev–Slobodetskii space and describe its general solution for some cases. This description is based on some distributions supported on a conical surface. For certain conical surfaces we describe such distributions. It permits to use such distributions to refine a general solution.

COMMUNICATED BY:

• A. Soldatov

Keywords:

• Pseudo-differential equation
• elliptic symbol
• cone
• wave factorization
• general solution
• distribution

AMS SUBJECT CLASSIFICATIONS:

• Primary: 35S15
• Secondary: 42B37
• 46F10

Acknowledgments

The author is very grateful to referees for their timely and helpful comments.

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

V. B. Vasilyev  http://orcid.org/0000-0001-9351-8084