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Research
My field of research is geometric analysis in metric spaces, especially Sobolev spaces,
Orlic-Sobolev spaces and BV-functions. I'm interested in extension
domains, removable sets, pointwise behaviour of functions and
Hardy and Poincaré inequalities in these spaces.
Publications
- (with
Pekka Koskela and
Nageswari Shanmugalingam)
Removable sets for the Poincaré inequality on metric spaces.
Indiana Univ. Math. J. 49 (2000), no.1, 333--352.
- PhD thesis: Orlicz-Sobolev spaces on metric measure spaces.
Ann. Acad. Sci. Fenn. Math. Diss. No. 135 (2004)
(Send me email to get a paper version or a pdf-file.)
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Characterization of Orlicz-Sobolev space,
Ark. Mat. 45 (2007), no.1, 123--139.
- (with
Juha Kinnunen)
Pointwise behaviour of M^{1,1} Sobolev functions ,
Math. Z. 257 (2007), no.3, 613-630.
- (with Toni Heikkinen and
Pekka Koskela)
Sobolev-type spaces from generalized Poincaré inequalities,
Studia Math. 181 (2007), 1--16.
- (with
Juha Kinnunen,
Riikka Korte and
Nageswari Shanmugalingam)
Lebesgue points and capacities via boxing inequality in
metric spaces,
Indiana Univ. Math. J. 57 (2008), no.1, 401--430
- (with
Piotr Hajłasz and
Pekka Koskela)
Sobolev embeddings, extensions and measure density condition,
J. Funct. Anal. 254 (2008), no.5, 1217--1234
- (with
Piotr Hajłasz and
Pekka Koskela)
Measure density and extendability of Sobolev functions,
Rev. Mat. Iberoamericana 24 (2008), no.2, 645--669.
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Pointwise behaviour of Orlicz-Sobolev functions,
Ann. Mat. Pura Appl. 188 (2009), no.1, 35--59.
- (with
Juha Kinnunen,
Riikka Korte and
Nageswari Shanmugalingam)
The De Diorgi measure and an obstacle problem related to minimal
surfaces in metric spaces,
to appear in J. Math. Pures Appl.
Preprints
- (with
Riikka Korte and
Juha Lehrbäck)
The equivalence between pointwise Hardy inequalities and uniform fatness,
submitted, 2009.
- (with Toni Heikkinen)
Orlicz-Sobolev extensions and measure density condition,
submitted, 2009.
Heli's home page
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