P. Goldstein

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20132018

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5 papers · 1 filter

math.CA2018

Jacobians of $W^{1, p}$ homeomorphisms, case $p = [n /2]$

Paweł Goldstein, Piotr Hajłasz

We investigate a known problem whether a Sobolev homeomorphism between domains in $R^{n}$ can change sign of the Jacobian. The only case that remains open is when $f\in W^{1…

math.CA2018

$C^{1}$ mappings in $R^{5}$ with derivative of rank at most $3$ cannot be uniformly approximated by $C^{2}$ mappings with derivative of rank at most 3

Paweł Goldstein, Piotr Hajłasz

We find a counterexample to a conjecture of Gałęski by constructing for some positive integers $m < n$ a mapping $f \in C^{1} (R^{n}, R^{n})$ satisfying $\mathrm{rank}\, Df\…

math.CA2018

Topologically nontrivial counterexamples to Sard's theorem

Paweł Goldstein, Piotr Hajłasz, Pekka Pankka

We prove the following dichotomy: if $n = 2, 3$ and $f \in C^{1} (S^{n + 1}, S^{n})$ is not homotopic to a constant map, then there is an open set $Ω \subset S^{n + 1}$ …

math.CA2018

Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion

Paweł Goldstein, Piotr Hajłasz

In the paper we investigate continuity of Orlicz-Sobolev mappings $W^{1, P} (M, N)$ of finite distortion between smooth Riemannian $n$ -manifolds, $n \geq 2$ , under the assumption that…

math.CA2017

Finite distortion Sobolev mappings between manifolds are continuous

Paweł Goldstein, Piotr Hajłasz, Mohammad Reza Pakzad

We prove that if $M$ and $N$ are Riemannian, oriented $n$ -dimensional manifolds without boundary and additionally $N$ is compact, then Sobolev mappings $W^{1, n} (M, N)$ of finite dis…

Jacobians of W1,p homeomorphisms, case p=[n/2]

C1 mappings in R5 with derivative of rank at most 3 cannot be uniformly approximated by C2 mappings with derivative of rank at most 3

Topologically nontrivial counterexamples to Sard's theorem

Topological obstructions to continuity of Orlicz-Sobolev mappings of finite distortion

Finite distortion Sobolev mappings between manifolds are continuous

Jacobians of $W^{1, p}$ homeomorphisms, case $p = [n /2]$

$C^{1}$ mappings in $R^{5}$ with derivative of rank at most $3$ cannot be uniformly approximated by $C^{2}$ mappings with derivative of rank at most 3