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Some estimates for the mean curvature of graphs over domains in $R^n$
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8422-6140
1991 (English)In: Doklady. Mathematics, ISSN 1064-5624, E-ISSN 1531-8362, Vol. 42, no 2, p. 387-390Article in journal (Refereed) Published
Abstract [en]

Let f be a C2-solution in a domain ΩRn of the equation

where H is a nondecreasing function of a real variable. In the particular case H(t)=a+bt, b>0, the preceding differential equation describes the capillarity in a tube of liquid [cf. R. Finn, Z. Angew. Math. Mech. 61 (1981), no. 3, 165–173; MR0626020]. The author establishes that P|H[f(x)]|pdxcap(P,Ω;Ω), where Ω is the boundary of Ω and cap(P,Ω,Ω) is the conformal capacity of a condenser (P,Ω;Ω) [cf., e.g., Yu. G. Reshetnyak, Spatial mappings with bounded distortion (Russian), see p. 52, "Nauka'' Sibirsk. Otdel., Novosibirsk, 1982; MR0665590]. The author also obtains estimates of the form supxΩ{|H[f(x)]|⋅dist(x,Ω)}p/n (1pn) for some categories of domains.

Place, publisher, year, edition, pages
Springer Berlin/Heidelberg, 1991. Vol. 42, no 2, p. 387-390
Keywords [en]
mean curvature
National Category
Geometry Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-133951OAI: oai:DiVA.org:liu-133951DiVA, id: diva2:1065692
Available from: 2017-01-16 Created: 2017-01-16 Last updated: 2017-11-29Bibliographically approved

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