Katarzyna Mazowiecka

activity

20142026

most citedFractional div-curl quantities and applications to nonlocal geometric equations

38 citations · 46 across the 20 of their papers we have counts for

collaborators

23 papers

math.AP2026

On minimizing $W^{s, 1/ s}$ -maps between circles

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

For $s \in (1/4, 1)$ and any degree the only $W^{s, \frac{1}{s}}$ -minimizers for $S^{1} \to S^{1}$ maps are Blaschke products. This gives a resolution of Open Problems…

math.AP2026

Minimizing and non-minimizing degree one $W^{s, 1/ s}$ -harmonic maps between spheres

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

We show that $i d : S^{1} \to S^{1}$ is \emph{not} a minimizing $W^{s, \frac{1}{s}}$ -harmonic map for $s \in (0, \frac{1}{8}$ ). On the other hand, for $s \in (\frac{1}{3},…

math.AP2026

Min-max $n$ -harmonic maps of degree 1 with free-boundary into $S^{n - 1}$ in almost round balls

Dorian Martino, Katarzyna Mazowiecka, Rémy Rodiac

Let $n \geq 3$ and let $Ω \subset R^{n}$ be a $C^{1}$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of th…

math.AP2026

A remark on staircase laminates in restricted sets

Igor Buchowiec, Pholphum Kamthorntaksina, Katarzyna Mazowiecka +2

We slightly extend the convex integration via staircase laminate toolbox recently developed by Kleiner, Müller, Székelyhidi, and Xie. As an example we revisit the proof by Astala-F…

math.AP2026

Existence of nontrival $n$ -harmonic maps via min-max methods

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

For any $n \geq 3$ and any closed manifold $N$ with $π_{n + k} (N) \neq = {0}$ for some $k \geq 0$ , we establish the existence of nontrivial $n$ -harmonic maps from…

math.AP2025

Existence of minimal maps of degree one in $W^{\frac{1}{p}, p} (S^{1}, S^{1})$ for $p \in [p^{'}, 2]$ , where $p^{'} \approx 1.13924$

Tomasz Kostrzewa, Katarzyna Mazowiecka

In this note, we show how the results of Mazowiecka--Schikorra, combined with those of Bourgain--Brezis--Mironescu, imply the existence of minimal maps of degree one in $ W^{\frac{…

math.AP2025

Existence of infinitely many homotopy classes from $S^{3}$ to $S^{2}$ having a minimimzing $W^{s, \frac{3}{s}}$ -harmonic map

Adam Grzela, Katarzyna Mazowiecka

In 1998 T. Rivière proved that there exist infinitely many homotopy classes of $π_{3} (S^{2})$ having a minimizing 3-harmonic map. This result is especially surprising taking in…

math.AP2025

A weak energy identity for $(n + α)$ -harmonic maps with a free boundary in a sphere

Dorian Martino, Katarzyna Mazowiecka, Rémy Rodiac

In this article, we show that sequences of $(n + α)$ -harmonic maps with a free boundary in $S^{d - 1}$ , where $α$ is a parameter tending to zero, converge to a bubble tree. For…

math.AP2025

Vectorial Kato inequality for $p$ -harmonic maps with optimal constant

Andreas Gastel, Katarzyna Mazowiecka, Michał Miśkiewicz

We derive the sharp vectorial Kato inequality for $p$ -harmonic mappings. Surprisingly, the optimal constant differs from the one obtained for scalar valued $p$ -harmonic functions b…

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 $Ω \subset R^{n}$ we find a smooth, strongly polyconvex function $F : R^{M \times n} \to R$ and a Lipschitz map $u\…

math.AP2024

Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere

Antoine Detaille, Katarzyna Mazowiecka

In this note, we study non-uniqueness for minimizing harmonic maps from $B^{3}$ to $S^{2}$ . We show that every boundary map can be modified to a boundary map that admits multi…

math.AP2023

s-stability for W^{s,n/s}-harmonic maps in homotopy groups

Katarzyna Mazowiecka, Armin Schikorra

We study $s$ -dependence for minimizing $W^{s, n / s}$ -harmonic maps $u : S^{n} \to S^{ℓ}$ in homotopy classes. Sacks--Uhlenbeck theory shows that, for each $s$ , m…

math.AP2023

Regularity of minimizing $p$ -harmonic maps into spheres and sharp Kato inequality

Katarzyna Mazowiecka, Michał Miśkiewicz

We study regularity of minimizing $p$ -harmonic maps $u : B^{3} \to S^{3}$ for $p$ in the interval $[2, 3]$ . For a long time, regularity was known only for $p = 3$ (essenti…

math.AP2021

Quantitative characterization of traces of Sobolev maps

Katarzyna Mazowiecka, Jean Van Schaftingen

We give a quantitative characterization of traces on the boundary of Sobolev maps in $W ˙^{1, p} (M, N)$ , where $M$ and $N$ are compact Riem…

math.AP2021

A fractional version of Rivière's GL(N)-gauge

Francesca Da Lio, Katarzyna Mazowiecka, Armin Schikorra

We prove that for antisymmetric vectorfield $Ω$ with small $L^{2}$ -norm there exists a gauge $A \in L^{\infty} \cap W ˙^{1/2, 2} (R^{1}, G L (N))$ such that ${\rm div}_{\frac12}…

math.AP2020★ 4 cited

Minimal $W^{s, \frac{n}{s}}$ -harmonic maps in homotopy classes

Katarzyna Mazowiecka, Armin Schikorra

Let $Σ$ a closed $n$ -dimensional manifold, $N \subset R^{M}$ be a closed manifold, and $u \in W^{s, \frac{n}{s}} (Σ, N)$ for $s \in (0, 1)$ . We extend the monumen…

math.AP2019★ 1 cited

On the size of the singular set of minimizing harmonic maps into the 2-sphere in dimension four and higher

Katarzyna Mazowiecka, Michał Miśkiewicz, Armin Schikorra

We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n \geq 4$ . For minimizing harmonic maps $u \in W^{1, 2} (Ω, S^{2})$ from $n$ -dimensional…

math.AP2018★ 1 cited

On the size of the singular set of minimizing harmonic maps

Katarzyna Mazowiecka, Michał Miśkiewicz, Armin Schikorra

We consider minimizing harmonic maps $u$ from $Ω \subset R^{n}$ into a closed Riemannian manifold $N$ and prove: (1) an extension to $n \geq 4$ of Almgren and Lieb'…

math.AP2018

Boundary regularity for minimizing biharmonic maps

Katarzyna Mazowiecka

We prove full boundary regularity for minimizing biharmonic maps with smooth Dirichlet boundary conditions. Our result, similarly as in the case of harmonic maps, is based on the n…

math.AP2017★ 2 cited

Epsilon-regularity for p-harmonic maps at a free boundary on a sphere

Katarzyna Mazowiecka, Rémy Rodiac, Armin Schikorra

We prove an $ε$ -regularity theorem for vector-valued p-harmonic maps, which are critical with respect to a partially free boundary condition, namely that they map the boundary into…

math.AP2017★ 38 cited

Fractional div-curl quantities and applications to nonlocal geometric equations

Katarzyna Mazowiecka, Armin Schikorra

We investigate a fractional notion of gradient and divergence operator. We generalize the div-curl estimate by Coifman-Lions-Meyer-Semmes to fractional div-curl quantities, obtaini…

math.AP2014

A conditional regularity result for p-harmonic flows

Krystian Kazaniecki, Michał Łasica, Katarzyna Ewa Mazowiecka +1

We prove an $ε$ -regularity result for a wide class of parabolic systems $u_{t} - div (∣\nabla u ∣^{p - 2} \nabla u) = B (u, \nabla u)$ with the right hand side $B$ g…

math.AP2014

The Lavrentiev gap phenomenon for harmonic maps into spheres holds on a dense set of zero degree boundary data

Katarzyna Mazowiecka, Paweł Strzelecki

We prove that for each positive integer $N$ the set of smooth, zero degree maps $ψ : S^{2} \to S^{2}$ which have the following three properties: (1) there is a uniq…

On minimizing Ws,1/s-maps between circles

Minimizing and non-minimizing degree one Ws,1/s-harmonic maps between spheres

Min-max n-harmonic maps of degree 1 with free-boundary into Sn−1 in almost round balls

A remark on staircase laminates in restricted sets

Existence of nontrival n-harmonic maps via min-max methods

Existence of minimal maps of degree one in Wp1​,p(S1,S1) for p∈[p′,2], where p′≈1.13924

Existence of infinitely many homotopy classes from S3 to S2 having a minimimzing Ws,s3​-harmonic map

A weak energy identity for (n+α)-harmonic maps with a free boundary in a sphere

Vectorial Kato inequality for p-harmonic maps with optimal constant

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

Generic non-uniqueness of minimizing harmonic maps from a ball to a sphere

s-stability for W^{s,n/s}-harmonic maps in homotopy groups

Regularity of minimizing p-harmonic maps into spheres and sharp Kato inequality

Quantitative characterization of traces of Sobolev maps

A fractional version of Rivière's GL(N)-gauge

Minimal Ws,sn​-harmonic maps in homotopy classes

On the size of the singular set of minimizing harmonic maps into the 2-sphere in dimension four and higher

On the size of the singular set of minimizing harmonic maps

Boundary regularity for minimizing biharmonic maps

Epsilon-regularity for p-harmonic maps at a free boundary on a sphere

Fractional div-curl quantities and applications to nonlocal geometric equations

A conditional regularity result for p-harmonic flows

The Lavrentiev gap phenomenon for harmonic maps into spheres holds on a dense set of zero degree boundary data

On minimizing $W^{s, 1/ s}$ -maps between circles

Minimizing and non-minimizing degree one $W^{s, 1/ s}$ -harmonic maps between spheres

Min-max $n$ -harmonic maps of degree 1 with free-boundary into $S^{n - 1}$ in almost round balls

Existence of nontrival $n$ -harmonic maps via min-max methods

Existence of minimal maps of degree one in $W^{\frac{1}{p}, p} (S^{1}, S^{1})$ for $p \in [p^{'}, 2]$ , where $p^{'} \approx 1.13924$

Existence of infinitely many homotopy classes from $S^{3}$ to $S^{2}$ having a minimimzing $W^{s, \frac{3}{s}}$ -harmonic map

A weak energy identity for $(n + α)$ -harmonic maps with a free boundary in a sphere

Vectorial Kato inequality for $p$ -harmonic maps with optimal constant

Regularity of minimizing $p$ -harmonic maps into spheres and sharp Kato inequality

Minimal $W^{s, \frac{n}{s}}$ -harmonic maps in homotopy classes