Juha Kinnunen

Professor of Mathematics at Helsinki University of Technology. Address: Institute of Mathematics, P.O. Box 1100, FI-02015 HELSINKI UNIVERSITY OF TECHNOLOGY, Finland. Tel: +358 9 451 3041. E-mail: juha.kinnunen[]tkk.fi.

Research

Harmonic analysis (maximal functions, Muckenhoupt's weights, Calderon-Zygmund theory), nonlinear partial differential equations (degenerate elliptic and parabolic equations of second order) and analysis on metric spaces (Sobolev spaces on metric spaces and calculus of variations on metric spaces).

See also

• Website of Juha Kinnunen at the department.
• The nonlinear PDE group website.
• Graduate School in Mathematical Analysis and Its Applications.
• Research group on Harnack inequalities in analysis and partial differential Equations, NSF Network.
• Global and geometric aspects of nonlinear partial differential equations, ESF Network.
• Harmonic and Complex Analysis and its Applications, ESF Network.
• Spring school in harmonic analysis and PDE, Helsinki University of Technology, June 2-6, 2008.

Some research papers

• J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces, to appear in J. Math. Pures Appl.
• J. Kinnunen, T. Lukkari and M. Parviainen, An existence result for superparabolic functions, J. Funct. Anal. 258 (2010), 713-728.
• J. Kinnunen and R. Korte, Characterizations for Hardy's inequalities, Around the Research of Vladimir Maz'ya, International Mathematical Series, Vol 11 Laptev Ari (Ed.), 239-254, 2010.
• D. Aalto and J. Kinnunen, The discrete maximal operator in metric spaces, to appear in J. Anal. Math.
• J. Kinnunen and M. Parviainen, Stability for degenerate parabolic equations, to appear in Adv. Calc. Var.
• M. Ekonen, J. Kinnunen, N. Marola and C. Sbordone, On Beckenbach-Rado type integral inequalities, Ricerche Mat. 58 (2009), 43-61.
• D. Aalto and J. Kinnunen, Maximal functions in Sobolev spaces, Sobolev Spaces in Mathematics I, International Mathematical Series, Vol. 8 Maz'ya, Vladimir (Ed.), 25-68, Springer, 2008.
• J. Kinnunen and R. Korte, Characterizations of Sobolev inequalities on metric spaces, J. Math. Anal. Appl. 344 (2008), 1093-1104. arXiv:0709.1097v1.
• J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, Lebesgue points and capacities via boxing inequality in metric spaces, Indiana Univ. Math. J. 57 (2008), 401-430.
• J. Kinnunen and P. Lindqvist, Definition and properties of supersolutions to the porous medium equation, J. reine angew. Math. 618 (2008), 135-168.
• J. Kinnunen, On the definition and properties of superparabolic functions, RIMS Kokyuroku 1553, 33-43, Potential Theory and Related Fields, Research Institute of Mathematical Sciences, Kyoto University, 2007.
• J. Kinnunen and H. Tuominen, Pointwise behaviour of Sobolev functions whose gradient is integrable to power one , Math. Z. 257 (2007), 613-630.
• J. Kinnunen, N. Marola and O. Martio, Harnack's principle for quasiminimizers, Ricerche Mat. 56 (2007), 73-88.
• J. Kinnunen and T. Kuusi, Local behaviour of solutions of doubly nonlinear parabolic equations, Math. Ann. 337 (2007), 705-528.
• P. Harjulehto, J. Kinnunen and T. Lukkari, Unbounded supersolutions of nonlinear equations with nonstandard growth conditions, Bound. Value Probl. (2007), Article ID 48348, 20 pages.
• J. Kinnunen and P. Lindqvist, Pointwise behaviour of semicontinuous supersolutions to a quasilinear parabolic equation, Ann. Mat. Pura Appl. (4) 185 (2006), 411-435.
• J. Kinnunen and N. Shanmugalingam, Polar sets on metric spaces, Trans. Amer. Math. Soc. 358 (2006), 11-37.
• J. Kinnunen and P. Lindqvist, Summability of semicontinuous supersolutions to a quasilinear parabolic equation, Ann Sc. Norm. Super. Pisa Cl. Sci. (5) 4 (2005), 59-78.
• P. Harjulehto and J. Kinnunen, Differentiation bases for Sobolev functions on metric spaces, Publ. Mat. 48 (2004), 381-395.
• J. Kinnunen and O. Martio, Nonlinear potential theory on metric spaces, Illinois J. Math. 46 (2002), 857-883.
• J. Kinnunen and E. Saksman, Regularity of the fractional maximal function, Bull. London Math. Soc. 35 (2003), 529-535.
• J. Kinnunen and J.L. Lewis, Very weak solutions of parabolic systems of p-Laplacian type, Ark. Mat. 40 (2002), 105-132.
• J. Kinnunen and V. Latvala, Lebesgue points for Sobolev functions on metric spaces, Revista Mat. Iberoamericana 18 (2002), 105-132.
• J. Kinnunen, Minimal, maximal and reverse Hölder inequalities, Papers on Analysis: A volume dedicated to Olli Martio on the occasion of his 60th birthday, Report, Univ. Jyväskylä 83 (2001), 225-247.
• J. Kinnunen and N. Shanmugalingam, Regularity of quasi-minimizers on metric spaces, Manuscripta Mathematica 105 (2001), 401-423.
• J. Kinnunen and J.L. Lewis, Higher integrability for parabolic systems of p-Laplacian type, Duke Math. J. 102 (2000), 253-271.
• J. Kinnunen and O. Martio, Choquet property for the Sobolev capacity in metric spaces, Proceedings on Analysis and Geometry (Novosibirsk Akademgorodok, 1999), 285-290, Izdat. Ross. Akad. Nauk Sib. Otd. Inst. Mat., Novosibirsk, 2000.
• J. Kinnunen and S. Zhou, A local estimate for nonlinear equations with discontinuous coefficients, Comm. Partial Differential Equations 24 (1999), 2043-2068.
• P. Hajlasz and J. Kinnunen, Hölder quasicontinuity of Sobolev functions on metric spaces, Revista Mat. Iberoamericana 14 (1998), 601-622.
• J. Kinnunen and P. Lindqvist, The derivative of the maximal function, J. reine angew. Math. 503 (1998), 161-167.
• J. Kinnunen and O. Martio, Hardy's inequalities for Sobolev functions, Math. Research Letters, 4 (1997), 489-500.
• J. Kinnunen, The Hardy-Littlewood maximal function of a Sobolev function, Israel J. Math., 100 (1997), 117-124.

Vita

• A brief curriculum vitae.
• A complete list of publications.

Graduate students (students marked by * are co-adviced by Professor Peter Hästö)

• Daniel Aalto, Phil. Lic. 2008
• Lauri Berkovits*
• Heikki Hakkarainen*
• Anne Heikkilä*
• Riikka Korte, Ph.D. 2008
• Tuomo Kuusi, Ph.D. 2007
• Teemu Lukkari. Ph.D. 2008
• Outi Elina Maasalo, Ph.D. 2008
• Niko Marola, Ph.D. 2007
• Mathias Masson
• Matti Nuortio*, Phil. Lic. 2008
• Mikko Parviainen, Ph.D. 2007
• Juhana Siljander
• Katja Tuhkanen*, Phil. Lic.

Opetus

Kandidaatintyöt, diplomityöt ja väitöskirjat

Matemaattisen analyysin erikoiskursseja

Mahdollisia aiheita ovat:

• analyysi metrisessä avaruudessa
• Fourierin analyysi
• geometrinen mittateoria
• harmoninen analyysi
• kompleksianalyysi
• osittaisdifferentiaaliyhtälöt ja
• potentiaaliteoria

Analyysi I, syksy 2009

• Kurssi Nopassa

• Kurssiesite

Analyysin lukupiiri, syksy 2009

• Kurssi Nopassa
• Esite

Epälineaariset osittaisdifferentiaaliyhtälöt, kevät 2010

• Kurssi Nopassa

• Kurssiesite