Alexander Ukhlov

collaborators

2 papers

math.AP2019

Quasiconformal Mappings and Neumann Eigenvalues of Divergent Elliptic Operators

Vladimir Gol'dshtein, Valeryi Pchelintsev, Alexander Ukhlov

We study spectral properties of divergence form elliptic operators $- div [A (z) \nabla f (z)]$ with the Neumann boundary condition in planar domains (including some fractal…

math.FA2013

Sobolev homeomorphisms and Brennan's conjecture

Vladimir Gol'dshtein, Alexander Ukhlov

Let $Ω \subset R^{n}$ be a domain that supports the $p$ -Poincaré inequality. Given a homeomorphism $φ \in L_{p}^{1} (Ω)$ , for $p > n$ we show the domain $φ (Ω)$ has finite geodesic di…