MODULUS AND CONTINUOUS CAPACITY

By S. Kallunki, Nageswari Shanmugalingam. 2001

71 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/6b044dbcd6f1da3c678c96c5d4b4caa304923456

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Citations in the corpus

The BV-capacity in metric spaces (2010, background): “During the past fifteen years, capacities in metric measure spaces have been studied, for example, in [11, 20, 21, 16].”
Modulus and the Poincaré inequality on metric measure spaces (2003, background): “Kallunki and Shanmugalingam [ KS01 ] do not restrict their attention to metric measure spaces with finite total mass, but instead consider metric measure spaces which admit a Poincar´ e inequality.”
POTENTIAL THEORY OF QUASIMINIMIZERS (2003, background): “Cp i E(t;r) ¢ • (1 +") p Z X g p u d„: 486 Juha Kinnunen and Olli Martio Now X is proper and thus admissible Lipschitz functions are dense in the class of admissible functions for E(r), see [ KaS ].”
The Perron method for p-harmonic functions in metric spaces (2003, unknown): “1 of Kallunki–Shanmugalingam [16] we see that u ∈ N(X) with ∫”
Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology (2012, methodology): “ith an application of our theory to condenser capacities. On metric spaces, such capacities have been used and studied under various assumptions by e.g. Heinonen–Koskela [22], Kallunki–Shanmugalingam [23] and Adamowicz–Bj¨orn–Bjo¨rn–Shanmugalingam [1]. Deﬁnition 5.12. Let Ω ⊂ Xbe a nonempty bounded ”
Geometric Implications of the Poincaré Inequality (2007, methodology): “of X. Then, in the definition of capp(E,F), we can restrict to locally Lipschitz functions u. For the proof, see [ 13 ].”
Prime ends for domains in metric spaces (2012, methodology): “ (quasi)conformal and quasiregular maps. Further applications of the p-modulus include its relation to capacities and Loewner spaces. See Va¨is¨al¨a [71], Heinonen–Koskela[36], Kallunki–Shanmugalingam[44], Vuorinen [73], and Lemma A.1. For nonempty sets U ⊂ X, E ⊂ U and F ⊂ U, we let Γ(E,F,U) denote”
Lebesgue points and capacities via the boxing inequality in metric spaces (2008, methodology): “It has been shown by Kallunki and Shanmugalingam in [ KS ] that if X is a proper quasiconvex metric measure space equipped with a doubling measure and supporting a weak (1,p)-Poincar´e inequality, then for any compact set K X ,w e have”