Toggle navigation
Armin Schikorra
Home
Publications
Teaching
Undergraduate Projects
Funding
Contact
Publications
All
Geometric PDE
Harmonic Analysis
Quantitative Topology
Nonsmooth Analysis
Calculus of Variations
PDE
Undergraduate Research
Convex minimizing curves of the scaling-invariant nonlocal Willmore energy
February, 2024
Giovanni Giacomin, Armin Schikorra
Preprint
Details
arXiv
Stirring coffee. A real-life application of Topology in Analysis
January, 2024
Armin Schikorra
Delta
(accepted)
Details
PDF
arXiv
Journal
Calderon-Zygmund theory for strongly coupled linear system of nonlocal equations with Holder-regular coefficient
January, 2024
Tadele Mengesha, Armin Schikorra, Adisak Seesanea, Sasikarn Yeepo
Preprint
Details
arXiv
s-stability for W^{s,n/s}-harmonic maps in homotopy groups
August, 2023
Katarzyna Mazowiecka, Armin Schikorra
preprint
Details
arXiv
A fractional Willmore-type energy functional - subcritical observations
June, 2023
Simon Blatt, Giovanni Giacomin, Julian Scheuer, Armin Schikorra
MATRIX Annals
(accepted)
Details
arXiv
Regularizing properties of n-Laplace systems with antisymmetric potentials in Lorentz spaces
May, 2023
Dorian Martino, Armin Schikorra
Math. Ann.
(accepted)
Details
arXiv
Journal
On the Gromov Non-Embedding theorem
March, 2023
Piotr Hajlasz, Armin Schikorra
Preprint
Details
arXiv
On uniqueness for half-wave maps in dimension d >= 3
November, 2022
Eugene Eyeson, Silvino Reyes Farina, Armin Schikorra
Trans. Am. Math. Soc.
Ser. B 11, 508-539 (2024).
Details
arXiv
Journal
Global tangential Calderon-Zygmund type estimates for the regional fractional Laplacian
September, 2022
Sujin Khomrutai, Armin Schikorra, Adisak Seesanea, Sasikarn Yeepo
Preprint
Details
arXiv
Nonlocal Bounded Variations with Applications
August, 2022
Harbir Antil, Hugo Díaz, Tian Jing, Armin Schikorra
SIAM Journal on Mathematical Analysis
56(6), 1903-1935, 2024
Details
arXiv
Journal
Quantitative estimates for fractional Sobolev mappings in rational homotopy groups
July, 2022
Woongbae Park, Armin Schikorra
Nonlinear Analysis
(235), October 2023, 113349
Details
arXiv
Journal
Carnot-Caratheodory and Koranyi-Geodesics in the Heisenberg Group
June, 2022
Josh Ascher, Armin Schikorra
Mathematics Exchange
Fall 2022, Volume 16, No. 1
Details
arXiv
Journal
Calderon-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient
September, 2021
Mouhamed Moustapha Fall, Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo
Partial Differential Equations and Applications
(accepted)
Details
arXiv
Journal
Bourgain-Brezis-Mironescu Convergence via Triebel-Lizorkin Spaces
September, 2021
Denis Brazke, Armin Schikorra, Po Lam Yung
Calc.Var.PDE
62, Article number: 41 (2023)
Details
arXiv
Journal
Scale-invariant tangent-point energies for knots
April, 2021
Simon Blatt, Philipp Reiter, Armin Schikorra, Nicole Vorderobermeier
preprint
Details
arXiv
Approximation of fractional harmonic maps
April, 2021
Harbir Antil, Sören Bartels, Armin Schikorra
IMA Journal of Numerical Analysis
(accepted)
Details
arXiv
Journal
A brief introduction to game theory and its potential implications for the economics of orthotics & prosthetics
March, 2021
Goeran Fiedler, Armin Schikorra
Canadian Prosthetics & Orthotics Journal
. 2021; Volume 4, Issue 2 (invited contribution)
Details
Journal
Fractional Sobolev Isometric Immersions of Planar Domains
March, 2021
Siran Li, Mohammad Reza Pakzad, Armin Schikorra
Ann. Sc. Norm. Sup. Pisa - Classe di Scienze
(accepted)
Details
arXiv
Journal
A fractional version of Riviere's GL(N)-gauge
January, 2021
Francesca Da Lio, Katarzyna Mazowiecka, Armin Schikorra
Annali di Matematica Pura ed Applicata
(accepted)
Details
arXiv
Journal
Non-blowup at critical exponent for a semilinear nonlocal diffusion equation
December, 2020
Sujin Khomrutai, Auttawitch Manui, Armin Schikorra
Appl. Math. Lett.
116 (2021)
Details
Journal
Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note
November, 2020
Armin Schikorra, James M. Scott
Studia. Math.
269 (2023), no. 3, 241-260.
Details
arXiv
Journal
On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations
July, 2020
Sasikarn Yeepo, Wicharn Lewkeeratiyutkul, Sujin Khomrutai, Armin Schikorra
Comm.Pure Applied Anal.
2021, 20(9): 2915-2939
Details
arXiv
Journal
Minimal $W^{s,n/s}$-harmonic maps in homotopy classes
June, 2020
Katarzyna Mazowiecka, Armin Schikorra
Journal of the London Mathematical Society (accepted)
Details
arXiv
Journal
On a Fractional Version of a Murat Compactness Result and Applications
April, 2020
Harbir Antil, Carlos N. Rautenberg, Armin Schikorra
SIAM J. Math. Anal.
53 (2021), no. 3, 3158–3187
Details
arXiv
Journal
Calderon-Zygmund type estimates for nonlocal PDE with Hoelder continuous kernel
February, 2020
Tadele Mengesha, Armin Schikorra, Sasikarn Yeepo
Advances in Mathematics
383 (2021), 107692
Details
arXiv
Journal
Partial Regularity for fractional harmonic maps into spheres
September, 2019
Vincent Millot, Marc Pegon, Armin Schikorra
Arch.Rat.Mech.Anal.
242 (2021), no. 2, 747–825
Details
arXiv
On symmetry of traveling solitary waves for dispersion generalized NLS
August, 2019
Lars Bugiera, Enno Lenzmann, Armin Schikorra, Jérémy Sok
Nonlinearity
33 (2020), no. 6, 2797–2819
Details
arXiv
Journal
W(s,n/s)-maps with positive distributional Jacobians
May, 2019
Siran Li, Armin Schikorra
Pot.A.
55, pages 403–417 (2021)
Details
PDF
arXiv
Journal
On O'hara knot energies I: Regularity for critical knots
May, 2019
Simon Blatt, Philipp Reiter, Armin Schikorra
J. Differential Geom.
121 (2022), no. 3, 385-424
Details
arXiv
Journal
An estimate of the Hopf degree of fractional Sobolev mappings
April, 2019
Armin Schikorra, Jean Van Schaftingen
Proc.AMS
148 (2020), 2877–2891
Details
arXiv
Journal
On BMO and Carleson measures on Riemannian Manifolds
March, 2019
Denis Brazke, Armin Schikorra, Yannick Sire
International Mathematics Research Notices
Details
arXiv
Journal
On the size of the singular set of minimizing harmonic maps
February, 2019
Katarzyna Mazowiecka, Michal Miskiewicz, Armin Schikorra
Memoirs of the AMS
(accepted)
Details
arXiv
Journal
Limits of conformal immersions under a bound on a fractional normal curvature quantity
December, 2018
Armin Schikorra
Vietnam Journal of Mathematics
(Special Issue on the occasion of J. Jost’s birthday), volume 49, pages 281–317 (2021)
Details
arXiv
Journal
On the size of the singular set of minimizing harmonic maps into the sphere in dimension three
November, 2018
Katarzyna Mazowiecka, Michal Miskiewicz, Armin Schikorra
Preprint
Details
arXiv
On C^{1,alpha}-regularity for critical points of a geometric obstacle-type problem
November, 2018
Sujin Khomrutai, Armin Schikorra
J. Math. Pures Appl.
(9) 136 (2020)
Details
arXiv
Journal
A remark on C^{1,alpha}-regularity for differential inequalities in viscosity sense
November, 2018
Armin Schikorra
Preprint
Details
arXiv
Holder-Topology of the Heisenberg group
October, 2018
Armin Schikorra
Aequationes mathematicae, 94(2), 323–343
Details
arXiv
Journal
Three examples of Sharp Commutator Estimates via Harmonic Extensions
July, 2018
Armin Schikorra
Taiwanese Journal of Mathematics - Volume 23, Number 6 (2019), 1365-1388.
Details
arXiv
Journal
Higher Hölder regularity for the fractional p−Laplacian in the superquadratic case
December, 2017
Lorenzo Brasco, Erik Lindgren, Armin Schikorra
Adv. Math. 338 (2018), pp. 782-846
Details
arXiv
Journal
New Directions in Geometric and Applied Knot Theory
December, 2017
Simon Blatt (ed), Philipp Reiter (ed), Armin Schikorra (ed)
DeGruyter
Details
Journal
On regularity theory for n/p-harmonic maps into manifolds
September, 2017
Francesca Da Lio, Armin Schikorra
Nonlinear Analysis
165 (2017), pp. 182-197
Details
arXiv
Journal
Epsilon-regularity for p-harmonic maps at a free boundary on a sphere
August, 2017
Katarzyna Mazowiecka, Rémy Rodiac, Armin Schikorra
APDE, Vol. 13 (2020), No. 5, 1301–1331
Details
arXiv
Journal
Boundary equations and regularity theory for geometric variational systems with Neumann data
June, 2017
Armin Schikorra
Arch. Rat. Mech. Anal
229(2), pp. 709-788, 2018
Details
arXiv
Journal
Fractional div-curl quantities and applications to nonlocal geometric equations
May, 2017
Katarzyna Mazowiecka, Armin Schikorra
J. Funct. Anal.
275 (2018), no. 1, 1–44.
Details
arXiv
Journal
On energy-critical half-wave maps into S^2
March, 2017
Enno Lenzmann, Armin Schikorra
Invent. Math.
213 (2018), no. 1, 1–82
Details
arXiv
Journal
Sharp commutator estimates via harmonic extensions
December, 2016
Enno Lenzmann, Armin Schikorra
Nonlinear Analysis
, 193, April 2020
Details
PDF
arXiv
Journal
Regularity for a fractional p-Laplace equation
August, 2016
Armin Schikorra, Tien-Tsan Shieh, Daniel Spector
Commun. Contemp. Math.
, 20 (01), 2018
Details
PDF
Project
Invitation to H-systems in higher dimensions: known results, new facts, and related open problems
June, 2016
Paweł Strzelecki, Armin Schikorra
EMS Surv. Math. Sci.
4 (2017), no. 1, 21–42.
Details
PDF
Weak solutions of geometric flows associated to integro-differential harmonic maps
December, 2015
Armin Schikorra, Yannick Sire, Changyou Wang
manuscripta math
153 (2017), no. 3-4, 389–402
Details
PDF
Nonlinear commutators for the fractional p-Laplacian and applications
June, 2015
Armin Schikorra
Math. Ann.
366(1), 695–720, (2016)
Details
arXiv
Journal
Lp-theory for fractional gradient PDE with VMO coefficients
March, 2015
Armin Schikorra, Tien-Tsan Shieh, Daniel Spector
Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl.
26 (2015), no. 4, 433–443
Details
PDF
Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension
February, 2015
Ali Maalaoui, Luca Martinazzi, Armin Schikorra
Comm.PDE
41 (2016), no. 10, 1593–1618
Details
PDF
An L1-type estimate for Riesz potentials
May, 2014
Armin Schikorra, Daniel Spector, Jean Van Schaftingen
Rev. Mat. Ibero
33 (2017), no. 1, 291-304
Details
PDF
Lp-gradient-harmonic maps into spheres and SO(N)
January, 2014
Armin Schikorra
Differential and Integral Equations
, Vol 28 (3 /4), pp. 383-408 (2015)
Details
PDF
Journal
Integro-differential harmonic maps into spheres
January, 2014
Armin Schikorra
Comm.PDE
40(3), 506-539 (2015)
Details
PDF
A notion of nonpositive curvature for general metric spaces
January, 2014
Miroslav Bačák, Bobo Hua, Jürgen Jost, Martin Kell, Armin Schikorra
Differential Geometry and its Applications
(2015), 22–32.
Details
PDF
A game-theoretic proof of convexity preserving properties for motion by curvature
January, 2014
Qing Liu, Armin Schikorra, Xiaodan Zhu
Indiana Univ. Math. J.
65(1) (2016), 171-197
Details
PDF
Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups
January, 2013
Piotr Hajłasz, Jeremy T. Tyson, Armin Schikorra
Geom. Funct. Anal.
24 (2014), pp.245-268
Details
arXiv
Journal
Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
January, 2013
Piotr Hajłasz, Armin Schikorra
Annales Academiae Scientiarum Fennicae
, 39 (2014), pp. 1-12
Details
PDF
General existence of solutions to dynamic programming principle
January, 2013
Qing Liu, Armin Schikorra
Comm. Pure and Applied Analysis.
14 (2015), no. 1, 167–184
Details
PDF
A note on zero sets of fractional sobolev functions with negative power of integrability
January, 2013
Armin Schikorra
Proc. Amer. Math. Soc.
143 (2015), no. 3, pp. 1189-1197
Details
PDF
A Game-Tree approach to discrete infinity Laplacian with running costs
January, 2013
Qing Liu, Armin Schikorra
Preprint, unpublished, arXiv:1305.7372
Details
PDF
n/p-harmonic maps: regularity for the sphere case
January, 2012
Francesca Da Lio, Armin Schikorra
Advances in Calculus of Variations
, Vol. 7, pp. 1-26
Details
PDF
epsilon-regularity for systems involving non-local, antisymmetric operators
January, 2012
Armin Schikorra
Calc. Var. P.D.E.
54(4),3531-3570, (2015)
Details
PDF
Harmonic analysis meets critical knots (Stationary points of the Moebius energy are smooth)
November, 2011
Simon Blatt, Philipp Reiter, Armin Schikorra
Trans. Amer. Math. Soc.
368 (2016), 6391-6438
Details
PDF
arXiv
Journal
Interior and Boundary-Regularity for Fractional Harmonic Maps on Domains
January, 2011
Armin Schikorra
(unpublished)
Details
PDF
A Note on Regularity for the n-dimensional H-System assuming logarithmic higher Integrability
December, 2010
Armin Schikorra
Analysis
Vol. 33, Issue 3 (2013)
Details
PDF
Regularity of n/2 harmonic maps into spheres
September, 2010
Armin Schikorra
Journal of Differential Equations
252 (2012) 1862–1911
Details
PDF
A Remark on Gauge Transformations and the Moving Frame Method
September, 2008
Armin Schikorra
Ann.Institute H.Poincare ( C )
, 27 (2010), pp. 503-515
Details
PDF
Journal
Boundary regularity via Uhlenbeck-Riviere decomposition
January, 2008
Frank Müller, Armin Schikorra
Analysis
, 29 (2009), pp. 199-220
Details
PDF
Erhaltungssätze in der Regularitätstheorie nichtlinearer elliptischer Systeme in zwei Dimensionen
November, 2007
Armin Schikorra
(Diplomarbeit / Master’s thesis)
Details
PDF