Juha Kinnunen

Professor of Mathematics at Helsinki University of Technology. Address: Aalto University, School of Science and Technology, Department of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland. Tel: +358 9 470 23041. E-mail: juha.kinnunen[]tkk.fi.

The nonlinear PDE group website

Teaching/Opetus

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.
• Evolutionary Problems, Institut Mittag-Leffler, Fall 2013.
• Graduate School in Mathematical Analysis and Its Applications.
• Analysis and Applications, Scandinavian Network.
• 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, A. Lorent and N. Shanmugalingam, Regularity of sets with quasiminimal boundary surfaces in metric spaces, submitted.
• J. Kinnunen, R. Korte, T. Kuusi and M. Parviainen, Nonlinear parabolic capacity and polar sets of superparabolic functions, submitted.
• J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, Pointwise properties of functions of bounded variation in metric spaces, submitted.
• J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, A characterization of Newtonian functions with zero boundary values, to appear in Calc. Var. Partial Differential Equations.
• D. Aalto and J. Kinnunen, The discrete maximal operator in metric spaces, J. Anal. Math. 111 (2010), 369-390.
• J. Kinnunen, R. Korte, N. Shanmugalingam and H. Tuominen, The De Giorgi measure and an obstacle problem related to minimal surfaces in metric spaces, J. Math. Pures Appl. 93 (2010), 599-622.
• H. Hakkarainen and J. Kinnunen, The BV-capacity in metric spaces, Manuscripta Math. 132 (2010), 51-73.
• 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.
• J. Kinnunen and M. Parviainen, Stability for degenerate parabolic equations, Adv. Calc. Var. 3 (2010), 29-48.
• 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 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 Math. 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, PhD 2010
• Lauri Berkovits*, Phil. Lic. 2010
• Heikki Hakkarainen*, PhD 2011
• Anne Heikkilä*, Phil. Lic. 2010
• Riikka Korte, PhD 2008
• Tuomo Kuusi, PhD 2007
• Panu Lahti, MSc 2011
• Teemu Lukkari. PhD 2008
• Outi Elina Maasalo, PhD 2008
• Niko Marola, PhD 2007
• Mathias Masson, Phil. Lic. 2010
• Matti Nuortio*, PhD 2011
• Mikko Parviainen, PhD 2007
• Parantap Shukla
• Juhana Siljander, PhD 2010
• Katja Tuhkanen*, Phil. Lic.