Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Mazowiecka, Katarzyna"'
For any $M, n \geq 2$ and any open set $\Omega \subset \mathbb{R}^n$ we find a smooth, strongly polyconvex function $F\colon \mathbb{R}^{M\times n}\to \mathbb{R}$ and a Lipschitz map $u\colon \mathbb{R}^n \to \mathbb{R}^M$ that is a weak local minimi
Externí odkaz:
http://arxiv.org/abs/2405.17084
In this note, we study non-uniqueness for minimizing harmonic maps from $B^3$ to $\mathbb{S}^2$. We show that every boundary map can be modified to a boundary map that admits multiple minimizers of the Dirichlet energy by a small $W^{1,p}$-change for
Externí odkaz:
http://arxiv.org/abs/2403.12662
We study $s$-dependence for minimizing $W^{s,n/s}$-harmonic maps $u\colon \mathbb{S}^n \to \mathbb{S}^\ell$ in homotopy classes. Sacks--Uhlenbeck theory shows that, for each $s$, minimizers exist in a generating subset of $\pi_{n}(\mathbb{S}^\ell)$.
Externí odkaz:
http://arxiv.org/abs/2308.14620
We study regularity of minimizing $p$-harmonic maps $u \colon B^3 \to \mathbb{S}^3$ for $p$ in the interval $[2,3]$. For a long time, regularity was known only for $p = 3$ (essentially due to Morrey) and $p = 2$ (Schoen-Uhlenbeck), but recently Gaste
Externí odkaz:
http://arxiv.org/abs/2302.06738
We give a quantitative characterization of traces on the boundary of Sobolev maps in $\dot{W}^{1,p}(\mathcal M, \mathcal N)$, where $\mathcal{M}$ and $\mathcal{N}$ are compact Riemannian manifolds, $\partial \mathcal{M} \neq \emptyset$: the Borel-mea
Externí odkaz:
http://arxiv.org/abs/2101.10934
We prove that for antisymmetric vectorfield $\Omega$ with small $L^2$-norm there exists a gauge $A \in L^\infty \cap \dot{W}^{1/2,2}(\mathbb{R}^1,GL(N))$ such that ${\rm div}_{\frac12} (A\Omega - d_{\frac{1}{2}} A) = 0$. This extends a celebrated the
Externí odkaz:
http://arxiv.org/abs/2101.07151
Let $\Sigma$ a closed $n$-dimensional manifold, $\mathcal{N} \subset \mathbb{R}^M$ be a closed manifold, and $u \in W^{s,\frac ns}(\Sigma,\mathcal{N})$ for $s\in(0,1)$. We extend the monumental work of Sacks and Uhlenbeck by proving that if $\pi_n(\m
Externí odkaz:
http://arxiv.org/abs/2006.07138
We extend the results of our recent preprint [arXiv: 1811.00515] into higher dimensions $n \geq 4$. For minimizing harmonic maps $u\in W^{1,2}(\Omega,\mathbb{S}^2)$ from $n$-dimensional domains into the two dimensional sphere we prove: (1) An extensi
Externí odkaz:
http://arxiv.org/abs/1902.03161
We consider minimizing harmonic maps $u$ from $\Omega \subset \mathbb{R}^n$ into a closed Riemannian manifold $\mathcal{N}$ and prove: (1) an extension to $n \geq 4$ of Almgren and Lieb's linear law. That is, if the fundamental group of the target ma
Externí odkaz:
http://arxiv.org/abs/1811.00515
Autor:
Mazowiecka, Katarzyna
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 nonexistence of nonconstant boundary tangent maps. With the help of rec
Externí odkaz:
http://arxiv.org/abs/1804.04545