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Rectifiability, interior approximation and harmonic measure

- M. Akman, S. Bortz, S. Hofmann, J. M. Martell
- MathematicsArkiv för Matematik
- 29 January 2016

We prove a structure theorem for any $n$-rectifiable set $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, satisfying a weak version of the lower ADR condition, and having locally finite $H^n$ ($n$-dimensional… Expand

A singular integral approach to a two phase free boundary problem

- S. Bortz, S. Hofmann
- Mathematics
- 20 May 2015

We present an alternative proof of a result of Kenig and Toro, which states that if $\Omega \subset \mathbb{R}^{n+1}$ is a two sided NTA domain, with Ahlfors-David regular boundary, and the $\log$ of… Expand

Zonal changes in renal structure and phospholipid metabolism in potassium-deficient rats.

- F. Toback, N. Ordóñez, S. Bortz, B. Spargo
- Biology, MedicineLaboratory investigation; a journal of technical…
- 1 February 1976

TLDR

Nonlocal self-improving properties: a functional analytic approach

- P. Auscher, S. Bortz, Moritz Egert, Olli Saari
- MathematicsTunisian Journal of Mathematics
- 19 July 2017

A functional analytic approach to obtaining self-improving properties of solutions to linear non-local elliptic equations is presented. It yields conceptually simple and very short proofs of some… Expand

Quantitative Fatou Theorems and Uniform Rectifiability

- S. Bortz, S. Hofmann
- MathematicsPotential Analysis
- 4 January 2018

We show that a suitable quantitative Fatou Theorem characterizes uniform rectifiability in the codimension 1 case.

Harmonic measure and approximation of uniformly rectifiable sets

- S. Bortz, S. Hofmann
- Mathematics
- 6 May 2015

Let $E\subset \mathbb{R}^{n+1}$, $n\ge 1$, be a uniformly rectifiable set of dimension $n$. We show $E$ that has big pieces of boundaries of a class of domains which satisfy a 2-sided corkscrew… Expand

On regularity of weak solutions to parabolic systems

- P. Auscher, S. Bortz, Moritz Egert, Olli Saari
- Mathematics
- 26 June 2017

Non-local Gehring lemmas

- P. Auscher, S. Bortz, Moritz Egert, Olli Saari
- Mathematics
- 7 July 2017

Non-local Gehring Lemmas in Spaces of Homogeneous Type and Applications

- P. Auscher, S. Bortz, Moritz Egert, Olli Saari
- MathematicsThe Journal of Geometric Analysis
- 7 July 2017

We prove a self-improving property for reverse Hölder inequalities with non-local right-hand side. We attempt to cover all the most important situations that one encounters when studying elliptic and… Expand

Reifenberg Flatness and Oscillation of the Unit Normal Vector

- S. Bortz, Max Engelstein
- Mathematics
- 17 August 2017

We show (under mild topological assumptions) that small oscillation of the unit normal vector implies Reifenberg flatness. We then apply this observation to the study of chord-arc domains and to a… Expand

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