2019
Том 71
№ 11

All Issues

Potemkin V. L.

Articles: 2
Article (Russian)

On the noncompactness of classes of mappings with restrictions on dilation in measure

Potemkin V. L., Ryazanov V. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 11. - pp. 1522–1531

We establish that the classes of mappings with restrictions in measure cannot be compact except for certain degenerate cases. In particular, this implies that any David class ΓI is noncompact.

Article (Russian)

On variations for mappings with restrictions on dilation in measure

Potemkin V. L.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 5. - pp. 716-718

We construct variations for classes of homeomorphisms with generalized derivatives in the case where restrictions in measure of general form are imposed on large values of dilation. We use the method for the construction of variations suggested by Gutlyanskii.