Riikka Korte
 Assistant professor
 Address:
Aalto University,
Department of Mathematics and Systems Analysis,
P.O. Box 11100,
00076 Aalto, Finland
 Visiting Address:
Otakaari 1, Espoo
Room M225
 Email: firstname.lastname@aalto.fi
 Phone: +358 50 453 2909
Research interests
I'm a member of
Nonlinear PDE research group.
My research area is mathematical analysis and nonlinear PDEs. More precisely, I'm interested in analysis on metric measure spaces and nonlinear parabolic (and ellpitic) partial differential equations (PDEs).
Students
I'm glad to discuss possible topics for Bachelor's, Master's or doctoral thesis.
Expecially for bachelor and diploma theses, the possible topics include for example analysis on metric measure spaces, harmonic analysis (maximal functions, Muckenhoput weights, BMO), nonlinear PDEs (Sobolev spaces, nonlinear elliptic or parabolic PDEs), calculus of variations, geometric measure theory (functions of bounded variation, minimal surfaces), but also other topics in analysis can be considered.
Please come and discuss any time I'm in my office M225 or send me an email to make an appointment.
Research papers
(A link to my papers in MathSciNet)
Keep in mind that some of the downloads of the following papers are earlier versions of the final articles and therefore may differ from the journal article.
2007
 Geometric implications of the Poincaré inequality,
Results Math., 50 (2007), no. 12, 93107.
Preprint.
2008
 Lebesgue points and capacities via the boxing inequality in metric spaces,
(with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen),
Indiana Univ. Math. J., 57(1), 401430, 2008.
Preprint.
 Characterizations of Sobolev inequalities on metric spaces,
(with Juha Kinnunen).
J. Math. Anal. Appl., 344(2), 10931103, 2008.
Preprint in arXiv.
 A Caccioppoli estimate and fine continuity for superminimizers on metric spaces.
Ann. Acad. Sci. Fenn. Math. 33 (2008), 597604.
Preprint.
2009
 Obstacle problem for nonlinear parabolic equations,
(with Tuomo Kuusi and Juhana Siljander).
J. Differential Equations 246 (9), 36683680, 2009.
Preprint.
2010
 Characterizations for Hardy's inequality,
(with Juha Kinnunen).
Around the Research of Vladimir Maz'ya I, International Mathematical Series, Vol. 11, Laptev Ari (Ed.), 239254, Springer, 2010.
 Equivalence and selfimprovement of pfatness and Hardy's inequality, and association with uniform perfectness,
(with Nageswari Shanmugalingam).
Math. Z. 246(1), 99110, 2010.
Preprint in arXiv.
 A note on the Wolff potential estimate for solutions to elliptic equations involving measures,
(with Tuomo Kuusi).
Adv. Calc. Var. March 2010. Vol. 3 No. 1:99113.
Preprint.
 A connection between a general class of superparabolic functions and supersolutions,
(with Tuomo Kuusi and Mikko Parviainen).
J. Evol. Equ. 10(1), 120, 2010.
Preprint.
 The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces,
(with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen).
J. Math. Pures Appl. 93 (2010), 599622.
 Stability of solutions of the double obstacle problem on metric spaces,
(with Michela Eleuteri, Zohra Farnana and Outi Elina Kansanen),
J. Anal. 18 (2010), 145160. (Proceedings of the ICM2010 Satellite Conference International workshop on Harmonic and Quasiconformal Mappings (HQM2010)).
2011
 Strong A_{∞}weights are A_{∞}weights on metric spaces,
(with Outi Elina Kansanen).
Revista Mat. Iberoamericana 27(1), 335354, 2011.
Preprint in arXiv.
 The equivalence between pointwise Hardy inequalities and uniform fatness,
(with Juha Lehrbäck and Heli Tuominen).
Math. Ann. 351 (2011), no. 3, 711731.
Preprint in arXiv.
2012
 A characterization of Newtonian functions with zero boundary values,
(with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen).
Calc. Var. PDE. 43 (2012), no. 3, 507528.
Preprint.
 Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property,
(with Niko Marola and Nageswari Shanmugalingam).
Ark. Mat., 50 (2012), 111134.
Preprint in CVGMT Pisa.
 Measure of curves in graded groups,
(with Valentino Magnani).
Illinois J. Math. 56 (2012), no. 2, 353366.
Preprint in CVGMT Pisa.
2013
 Nonlinear parabolic capacity and polar sets of superparabolic functions,
(with Juha Kinnunen, Tuomo Kuusi and Mikko Parviainen).
Math. Ann. 355 (2013), no. 4, 13491381.
Preprint.
 Regularity of sets with quasiminimal boundary surfaces in metric spaces,
(with Juha Kinnunen, Andrew Lorent and Nageswari Shanmugalingam).
J. Geom. Anal. 23 (2013), no. 4, 16071640.
Preprint.
2014
 On Whitneytype characterization of approximate differentiability on metric measure spaces, (with Estibalitz DurandCartagena, Lizaveta Ihnatsyeva and Marta Szumańska).
Canad. J. Math. (66) 2014, 721742.
Preprint.
 Relative isoperimetric inequalitites and sufficient conditions for finite perimeter on metric spaces,
(with Panu Lahti).
Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 1, 129154.
 Pointwise properties of functions of bounded variation in metric spaces,
(with Juha Kinnunen, Nageswari Shanmugalingam and Heli Tuominen). Rev. Mat. Complut. 27 (2014), no. 1, 4167.
Preprint.
2015
 A characterization of BMO selfmaps of a metric measure space,
(with Juha Kinnunen, Niko Marola, and Nageswari Shanmugalingam).
Collect. Math. (2015) 66:405421.
Preprint in arXiv.
 Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space,
(with Lizaveta Ihnatsyeva).
Math. Nachr. 288, No. 1112, 13031316 (2015).
Preprint in arXiv.
 Semmes family of curves and a characterization of functions of bounded variation in terms of curves,
(with Panu Lahti and Nageswari Shanmugalingam). Calc. Var. Partial Differential Equations 54 (2015), no. 2, 13931424.
Preprint in CVGMT.
 Stability and continuity of functions of least gradient,
(with Heikki Hakkarainen, Panu Lahti and Nageswari Shanmugalingam).
Anal. Geom. Metr. Spaces 3 (2015), 123139.
Preprint in arXiv.
2016
 Homeomorphisms of the Heisenberg group preserving BMO,
(with Niko Marola and Olli Saari).
Arch. Math. (Basel) 106 (2016), no. 2, 175182.
Preprint.
2017

Minima of quasisuperminimizers, (with Anders Björn and Jana Björn)
Preprint in arXiv.
Nonlinear Anal. 155 (2017) 264284.
2018
 The space JN_{p}: nontriviality and duality, (with Galia Dafni, Tuomas Hytönen, Hong Yue). J. Funct. Anal. 275 (2018), no. 3, 577603. Preprint in arXiv.
Accepted papers
 The higher integrability of weak solutions of porous medium systems, (with Verena Bögelein, Frank Duzaar and Christoph Scheven).
Adv. Nonlinear Anal. (to appear), 2018. Preprint.
 Notions of Dirichlet problem for functions of least gradient in metric measure spaces , (with Panu Lahti, Xining Li and Nageswari Shanmugalingam).
Revista Matematica Iberoamericana (to appear). Preprint in arXiv.
 Lower semicontinuous obstacles for the porous medium equation, (with Pekka Lehtelä, Stefan Sturm). J. Differential Equations (to appear), 2018. Preprint in arXiv.
 A maximal function approach to twomeasure Poincaré inequalities, (with Juha Kinnunen, Juha Lehrbäck and Antti V. Vähäkangas). The Journal of Geometric Analysis (to appear), 2018. Preprint in arXiv.
Submitted papers
 Equivalence of two BV classes of functions in metric spaces, and existence of a Semmes family of curves under a 1Poincaré inequality, (with Estibalitz DurandCartagena, Sylvester ErikssonBique and Nageswari Shanmugalingam). Preprint in arXiv.
Theses
Other