On an EVI curve characterization of Hilbert spaces

Max K. Von Renesse; Jonas M. Tölle

doi:10.1016/j.jmaa.2011.06.080

On an EVI curve characterization of Hilbert spaces

Max K. Von Renesse^*, Jonas M. Tölle

^*Tämän työn vastaava kirjoittaja

Ei julkaistu Aalto-yliopiston affiliaatiolla

Technical University of Berlin

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

2 Sitaatiot (Scopus)

Abstrakti

It is shown that the existence of a large enough collection of EVI (evolution variational inequality) curves for a lower semi-continuous functional on a Banach space implies that the space is in fact a Hilbert space. The main result is exemplified by the p-Laplacian evolution in Banach space.

Alkuperäiskieli	Englanti
Sivut	589-598
Sivumäärä	10
Julkaisu	Journal of Mathematical Analysis and Applications
Vuosikerta	385
Numero	1
DOI - pysyväislinkit	https://doi.org/10.1016/j.jmaa.2011.06.080
Tila	Julkaistu - 1 tammik. 2012
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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10.1016/j.jmaa.2011.06.080Lisenssi: Muu

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title = "On an EVI curve characterization of Hilbert spaces",

abstract = "It is shown that the existence of a large enough collection of EVI (evolution variational inequality) curves for a lower semi-continuous functional on a Banach space implies that the space is in fact a Hilbert space. The main result is exemplified by the p-Laplacian evolution in Banach space.",

keywords = "Characterizations of Hilbert spaces, Duality map, Evolution variational inequality, G{\^a}teaux subdifferentiable function, Gradient flow, Quasi-convex function",

author = "{Von Renesse}, {Max K.} and T{\"o}lle, {Jonas M.}",

year = "2012",

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doi = "10.1016/j.jmaa.2011.06.080",

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AU - Von Renesse, Max K.

AU - Tölle, Jonas M.

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N2 - It is shown that the existence of a large enough collection of EVI (evolution variational inequality) curves for a lower semi-continuous functional on a Banach space implies that the space is in fact a Hilbert space. The main result is exemplified by the p-Laplacian evolution in Banach space.

AB - It is shown that the existence of a large enough collection of EVI (evolution variational inequality) curves for a lower semi-continuous functional on a Banach space implies that the space is in fact a Hilbert space. The main result is exemplified by the p-Laplacian evolution in Banach space.

KW - Characterizations of Hilbert spaces

KW - Duality map

KW - Evolution variational inequality

KW - Gâteaux subdifferentiable function

KW - Gradient flow

KW - Quasi-convex function

UR - http://www.scopus.com/inward/record.url?scp=80051801425&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2011.06.080

DO - 10.1016/j.jmaa.2011.06.080

M3 - Article

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SN - 0022-247X

VL - 385

SP - 589

EP - 598

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

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On an EVI curve characterization of Hilbert spaces

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