49 citations · 101 across the 51 of their papers we have counts for
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Extension operators on Sobolev spaces with decreasing integrability
Alexander Ukhlov
We study extension operators on Sobolev spaces with decreasing integrability on the base of set functions associated with the operator norms. Sharp necessary conditions in the term…
Boundary Values of Functions of Dirichlet Spaces on Capacitary Boundaries
Vladimir Gol'dshtein, Alexander Ukhlov
We prove that any weakly differentiable function with square integrable gradient can be extended to a capacitary boundary of any simply connected plane domain exc…
Sobolev homeomorphisms and Poincare inequality
V. Gol'dshtein, A. Ukhlov
We study global regularity properties of Sobolev homeomorphisms on -dimensional Riemannian manifolds under the assumption of -integrability of its first weak derivatives in d…
Weighted Sobolev spaces and embedding theorems
V. Gol'dshtein, A. Ukhlov
In the present paper we study embedding operators for weighted Sobolev spaces whose weights satisfy the well-known Muckenhoupt A_p-condition. Sufficient conditions for boundedness…