Publications

Calderon-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient

Partial Differential Equations and Applications (accepted)

Preprint

preprint

preprint

A brief introduction to game theory and its potential implications for the economics of orthotics & prosthetics

Canadian Prosthetics & Orthotics Journal. 2021; Volume 4, Issue 2 (invited contribution)

Preprint

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

Annali di Matematica Pura ed Applicata (accepted)

Non-blowup at critical exponent for a semilinear nonlocal diffusion equation

Appl. Math. Lett. 116 (2021)

Weak Limits of Fractional Sobolev Homeomorphisms are Almost Injective: A Note

Studia. Math. (accepted)

On the Calderon-Zygmund property of Riesz-transform type operators arising in nonlocal equations

Comm.Pure Applied Anal. 2021, 20(9): 2915-2939

preprint

On a Fractional Version of a Murat Compactness Result and Applications

SIAM Journal on Mathematical Analysis (accepted)

Calderon-Zygmund type estimates for nonlocal PDE with Hoelder continuous kernel

Advances in Mathematics 383 (2021), 107692

Partial Regularity for fractional harmonic maps into spheres

Arch.Rat.Mech.Anal. (accepted)

On symmetry of traveling solitary waves for dispersion generalized NLS

Nonlinearity 33 (2020), no. 6, 2797–2819

W(s,n/s)-maps with positive distributional Jacobians

Pot.A. 55, pages 403–417 (2021)

On O'hara knot energies I: Regularity for critical knots

Journal Differential Geometry (accepted)

An estimate of the Hopf degree of fractional Sobolev mappings

Proc.AMS 148 (2020), 2877–2891

On BMO and Carleson measures on Riemannian Manifolds

International Mathematics Research Notices

On the size of the singular set of minimizing harmonic maps

Memoirs of the AMS (accepted)

Limits of conformal immersions under a bound on a fractional normal curvature quantity

Vietnam Journal of Mathematics (Special Issue on the occasion of J. Jost’s birthday), volume 49, pages 281–317 (2021)

Preprint

On C^{1,alpha}-regularity for critical points of a geometric obstacle-type problem

J. Math. Pures Appl. (9) 136 (2020)

Preprint

Holder-Topology of the Heisenberg group

Aequationes mathematicae, 94(2), 323–343

Three examples of Sharp Commutator Estimates via Harmonic Extensions

Taiwanese Journal of Mathematics - Volume 23, Number 6 (2019), 1365-1388.

Higher Hölder regularity for the fractional p−Laplacian in the superquadratic case

Adv. Math. 338 (2018), pp. 782-846

DeGruyter

On regularity theory for n/p-harmonic maps into manifolds

Nonlinear Analysis 165 (2017), pp. 182-197

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

APDE, Vol. 13 (2020), No. 5, 1301–1331

Boundary equations and regularity theory for geometric variational systems with Neumann data

Arch. Rat. Mech. Anal 229(2), pp. 709-788, 2018

Fractional div-curl quantities and applications to nonlocal geometric equations

J. Funct. Anal. 275 (2018), no. 1, 1–44.

On energy-critical half-wave maps into S^2

Invent. Math. 213 (2018), no. 1, 1–82

Sharp commutator estimates via harmonic extensions

Nonlinear Analysis, 193, April 2020

Regularity for a fractional p-Laplace equation

Commun. Contemp. Math., 20 (01), 2018

Invitation to H-systems in higher dimensions: known results, new facts, and related open problems

EMS Surv. Math. Sci. 4 (2017), no. 1, 21–42.

Weak solutions of geometric flows associated to integro-differential harmonic maps

manuscripta math 153 (2017), no. 3-4, 389–402

Nonlinear commutators for the fractional p-Laplacian and applications

Math. Ann. 366(1), 695–720, (2016)

Lp-theory for fractional gradient PDE with VMO coefficients

Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 26 (2015), no. 4, 433–443

Blow-up behaviour of a fractional Adams-Moser-Trudinger type inequality in odd dimension

Comm.PDE 41 (2016), no. 10, 1593–1618

An L1-type estimate for Riesz potentials

Rev. Mat. Ibero 33 (2017), no. 1, 291-304

Lp-gradient-harmonic maps into spheres and SO(N)

Differential and Integral Equations, Vol 28 (3 /4), pp. 383-408 (2015)

Integro-differential harmonic maps into spheres

Comm.PDE 40(3), 506-539 (2015)

A notion of nonpositive curvature for general metric spaces

Differential Geometry and its Applications (2015), 22–32.

A game-theoretic proof of convexity preserving properties for motion by curvature

Indiana Univ. Math. J. 65(1) (2016), 171-197

Homotopy groups of spheres and Lipschitz homotopy groups of Heisenberg groups

Geom. Funct. Anal. 24 (2014), pp.245-268

Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces

Annales Academiae Scientiarum Fennicae, 39 (2014), pp. 1-12

General existence of solutions to dynamic programming principle

Comm. Pure and Applied Analysis. 14 (2015), no. 1, 167–184

A note on zero sets of fractional sobolev functions with negative power of integrability

Proc. Amer. Math. Soc. 143 (2015), no. 3, pp. 1189-1197

A Game-Tree approach to discrete infinity Laplacian with running costs

Preprint, unpublished, arXiv:1305.7372

n/p-harmonic maps: regularity for the sphere case

Advances in Calculus of Variations, Vol. 7, pp. 1-26

epsilon-regularity for systems involving non-local, antisymmetric operators

Calc. Var. P.D.E. 54(4),3531-3570, (2015)

Harmonic analysis meets critical knots (Stationary points of the Moebius energy are smooth)

Trans. Amer. Math. Soc. 368 (2016), 6391-6438

(unpublished)

A Note on Regularity for the n-dimensional H-System assuming logarithmic higher Integrability

Analysis Vol. 33, Issue 3 (2013)

Regularity of n/2 harmonic maps into spheres

Journal of Differential Equations 252 (2012) 1862–1911

A Remark on Gauge Transformations and the Moving Frame Method

Ann.Institute H.Poincare ( C ), 27 (2010), pp. 503-515

Boundary regularity via Uhlenbeck-Riviere decomposition

Analysis, 29 (2009), pp. 199-220

Erhaltungssätze in der Regularitätstheorie nichtlinearer elliptischer Systeme in zwei Dimensionen

(Diplomarbeit / Master’s thesis)