Isoperimetric inequalities in potential theory

Hansen W, Nadirashvili N (1994)
Potential Analysis 3(1): 1-14.

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Autor*in
Hansen, WolfhardUniBi; Nadirashvili, N.
Abstract / Bemerkung
Given a non-empty bounded domain G in R(n), n greater-than-or-equal-to 2, let r0(G) denote the radius of the ball G0 having center 0 and the same volume as G. The exterior deficiency d(e)(G) is defined by d(e)(G) = r(e)(G)/r0(G) - 1 where r(e)(G) denotes the circumradius of G. Similarly d(i)(G) = 1 - r(i)(G)/r0(G) where r(i)(G) is the inradius of G. Various isoperimetric inequalities for the capacity and the first eigenvalue of G are shown. The main results are of the form Cap G greater-than-or-equal-to (1 + cf(d(e)(G))) greater-than-or-equal-to Cap G0 and lambda1(G) greater-than-or-equal-to (1 + cf(d(i)(G)))lambda1(G0), f(t) = t3 if n = 2, f(t) = t3/(ln 1/t) if n = 3, f(t) = t(n+3)/2 if n greater-than-or-equal-to 4 (for convex G and small deficiencies if n greater-than-or-equal-to 3).
Stichworte
ISOPERIMETRIC INEQUALITY; EIGENVALUE; DEFICIENCY; CAPACITY
Erscheinungsjahr
1994
Band
3
Ausgabe
1
Seite(n)
1-14
ISSN
0926-2601
Page URI
https://pub.uni-bielefeld.de/record/1643743

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Hansen W, Nadirashvili N. Isoperimetric inequalities in potential theory. Potential Analysis. 1994;3(1):1-14.
Hansen, W., & Nadirashvili, N. (1994). Isoperimetric inequalities in potential theory. Potential Analysis, 3(1), 1-14. doi:10.1007/BF01047833
Hansen, W., and Nadirashvili, N. (1994). Isoperimetric inequalities in potential theory. Potential Analysis 3, 1-14.
Hansen, W., & Nadirashvili, N., 1994. Isoperimetric inequalities in potential theory. Potential Analysis, 3(1), p 1-14.
W. Hansen and N. Nadirashvili, “Isoperimetric inequalities in potential theory”, Potential Analysis, vol. 3, 1994, pp. 1-14.
Hansen, W., Nadirashvili, N.: Isoperimetric inequalities in potential theory. Potential Analysis. 3, 1-14 (1994).
Hansen, Wolfhard, and Nadirashvili, N. “Isoperimetric inequalities in potential theory”. Potential Analysis 3.1 (1994): 1-14.