Yevgeniy Guseynov's research while affiliated with Policy Analysis Inc. and other places

Publications (3)

Article
For a given parameterization of a Jordan curve, we define the notion of summability or classes of measurable functions on a contour where a new integral is introduced. It is shown that natural functional spaces defining summability for non-rectifiable Jordan curves are the Lebesgue spaces with the weighted norm. For non-rectifiable Jordan curves wh...
Conference Paper
We are studying the layer potentials on rough boundaries in Rd, d>1, for Holder classes. The new surface integral introduced by the second author allows extend the layer potentials properties to highly irregular boundaries like non-rectifiable Jordan curves, fractals, sets of finite perimeter boundaries and flat chains. Such surfaces could have the...
Article
Full-text available
We define a surface integral over the boundary of open bounded sets in \( R^d,\ d\ge {}2\), and provide a criterion that completely describes all the boundaries where this integral exists for the \( (d-1\))-differential forms from Hölder classes. The surface integral and the Gauss–Green formula are used in many areas of mathematics and physics, and...

Citations

... The geometric concept of d-summable sets is due to Harrison and Norton [18] (see also [17]). A variation of it, the notion of h-summability, has just introduced in [3]. ...