A. Schikorra

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math.AP2026

HÃ¶lder maps under Pfaffian constraints

Armin Schikorra

Given a one form $I^»$ in $R^{N}$ and $f : S^{n} \to R^{N}$ with $f^{*} I^» = 0$ we discuss the maximal HÃ¶lder regularity of extensions $F: \mathbb{B}^{n+1} \t…

math.AP2024

A note on limiting Calderon-Zygmund theory for transformed $n$ -Laplace systems in divergence form

Dorian Martino, Armin Schikorra

We consider rotated $n$ -Laplace systems on the unit ball $B_{1} \subset R^{n}$ of the form \begin{align*} -\mathrm{div}\left( Q|\nabla u|^{n-2} \nabla u\right) = \mathrm{div}(…

math.AP2024

Failure of $L^{r}$ -CalderÃ³n-Zygmund estimates for the p-Laplace equation for small $r$

Armin Schikorra

Let $p \neq = 2$ . For any small enough $r > max {p - 1, 1}$ and for any $I^ > 1$ there exists a Lipschitz function $u$ and a bounded vectorfield $f$ such that \[ \begin{cases} {\rm div…

math.AP2024

A short note on nowhere smooth critical points of polyconvex functionals in arbitrary dimension

Katarzyna Mazowiecka, Armin Schikorra

For any $M, n \geq 2$ and any open set $I^c ◯ \subset R^{n}$ we find a smooth, strongly polyconvex function $F : R^{M \times n} \to R$ and a Lipschitz map $u…

math.AP2024

On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps

Silvino Reyes Farina, Armin Schikorra

We prove a priori estimates for wave systems of the type \[ \partial_{tt} u - Îu = Î©\cdot du + F(u) \quad \text{in $R^{d} \times R$ } \] where $d \geq 4$ and $I^c ◯$ …

HÃ¶lder maps under Pfaffian constraints

A note on limiting Calderon-Zygmund theory for transformed n-Laplace systems in divergence form

Failure of Lr-CalderÃ³n-Zygmund estimates for the p-Laplace equation for small r

A short note on nowhere smooth critical points of polyconvex functionals in arbitrary dimension

On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps

A note on limiting Calderon-Zygmund theory for transformed $n$ -Laplace systems in divergence form

Failure of $L^{r}$ -CalderÃ³n-Zygmund estimates for the p-Laplace equation for small $r$