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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2002, Volume 236, Pages 503–508 (Mi tm319)  
This article is cited in 7 scientific papers (total in 7 papers)

Harnack Inequalities on Recurrent Metric Fractals

U. Mosco

University of Rome "La Sapienza"
Full-text PDF (129 kB) Citations (7)
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Abstract: We introduce the notion of metric fractal and prove Harnack inequalities for metric fractals whose dimension is less than 2. The result applies, in particular, to finitely ramified fractals like the Sierpinski curves.
Received in November 2000
Bibliographic databases:
UDC: 517.9
Language: English
Citation: U. Mosco, “Harnack Inequalities on Recurrent Metric Fractals”, Differential equations and dynamical systems, Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 236, Nauka, MAIK «Nauka/Inteperiodika», M., 2002, 503–508; Proc. Steklov Inst. Math., 236 (2002), 490–495
Citation in format AMSBIB
\Bibitem{Mos02}
\by U.~Mosco
\paper Harnack Inequalities on Recurrent Metric Fractals
\inbook Differential equations and dynamical systems
\bookinfo Collected papers. Dedicated to the 80th anniversary of academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2002
\vol 236
\pages 503--508
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm319}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1931049}
\zmath{https://zbmath.org/?q=an:1125.31301}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2002
\vol 236
\pages 490--495
Linking options:
  • https://www.mathnet.ru/eng/tm319
  • https://www.mathnet.ru/eng/tm/v236/p503
    • This publication is cited in the following 7 articles:
    1. Timoshin S.A., “Axiomatic Regularity on Metric Spaces”, Michigan Mathematical Journal, 56:2 (2008), 301–313  crossref  mathscinet  zmath  isi  scopus
    2. Di Fazio G., Gutierrez C.E., Lanconelli E., “Covering theorems, inequalities on metric spaces and applications to PDE's”, Mathematische Annalen, 341:2 (2008), 255–291  crossref  mathscinet  zmath  isi  scopus
    3. Lancia M.R., Masamune J., “The Liouville property of unbounded fractal layers”, Complex Variables and Elliptic Equations, 53:4 (2008), 297–306  crossref  mathscinet  zmath  isi
    4. Mosco U., “Gauged Sobolev inequalities”, Applicable Analysis, 86:3 (2007), 367–402  crossref  mathscinet  zmath  isi
    5. Capitanelli R., “Harnack inequality for p–Laplacians associated to homogeneous p–Lagrangians”, Nonlinear Analysis–Theory Methods & Applications, 66:6 (2007), 1302–1317  crossref  mathscinet  zmath  isi  scopus
    6. Capitanelli R., “Harnack inequality for p-Laplacians on metric fractals”, Elliptic and Parabolic Problems - A SPECIAL TRIBUTE TO THE WORK OF HAIM BREZIS, Progress in Nonlinear Differential Equations and their Applications, 63, 2005, 119–126  crossref  mathscinet  zmath  isi  scopus
    7. Mosco U., “An elementary introduction to fractal analysis”, Nonlinear Analysis and Applications to Physical Sciences, 2004, 51–90  mathscinet  zmath  isi
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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