On a class of generalized functions arising in elasticity

Abstract

We consider a class of generalized functions arising in the theory of thin elastic shells. Such problems were studied in the works by Sanchez-Palencia and his collaborators. Moreover, such classes arise in many other problems of mathematical physics. The principal feature of these problems is the necessity of consideration of the elliptic boundary value problems with the violated Shapiro–Lopatinsky condition. It implies unsolvability of the problems in the distribution spaces. To solve such problems it is necessary to consider the generalized functions with exponentially growing Fourier transforms.

Keywords:

• generalized functions
• thin shells
• elasticity

AMS Subject Classifications::

• 30G05
• 46F05
• 74B05
• 34E05