Paweł Goldstein

Calderon-Zygmund type estimates for nonlinear systems with quadratic growth on the Heisenberg group

Abstract We prove the Calderón-Zygmund–type estimates for nonlinear subelliptic systems with quadratic growth, of the type with |A(z, ξ)| ≈ L(1 + |ξ|), where is the horizontal gradient on Heisenberg group. 2000 Mathematics Subject Classification: 35H20; 35B65.

A Measure and Orientation Preserving Homeomorphism with Approximate Jacobian Equal −1 Almost Everywhere

We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to −1 almost everywhere. Moreover, we prove that our homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms.

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

We find a counterexample to a conjecture of Ga{\l}\k{e}ski by constructing for some positive integers

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

m<n

On polyharmonic maps into spheres in the critical dimension

a mapping

A measure and orientation preserving homeomorphism of a cube with Jacobian equal

f\in C^1(\mathbb{R}^n,\mathbb{R}^n)

-1

satisfying

almost everywhere

\mathrm{rank}\, Df\leq m

Gradient flow of a harmonic function in R 3

that, even locally, cannot be uniformly approximated by

Topologically Nontrivial Counterexamples to Sard’s Theorem

C^2