Sobolev Spaces with Zero Boundary Values on Metric Spaces

By T. Kilpeläinen, Juha Kinnunen, O. Martio. 2000

123 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ca03d190d576b1bad043abf47d05f4c64d5b6191

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In Applied Mathematics

Citations in the corpus

Moser iteration for (quasi)minimizers on metric spaces (2006, unknown): “For this and other properties as well as equivalent deflnitions of the capacity we refer to Kilpel˜ ainen{ Kinnunen{Martio [ 23 ] and Kinnunen{Martio [24], [25].”
A weak Kellogg property for quasiminimizers (2006, methodology): “For this and other properties as well as equivalent definitions of the capacity we refer to Kilpeläinen–Kinnunen–Martio [19] and Kinnunen–Martio [20], [21].”
The Perron method for p-harmonic functions in metric spaces (2003, methodology): “Definition 2.4 The p-capacity of a Borel set E ⊂ X is the number Cp(E) = inf ‖u‖pN1,p(X), where the infimum is taken over all u ∈ N1,p(X) such that u = 1 on E. Remark 2.5 For equivalent definitions of the p-capacity we refer to Kilpeläinen– Kinnunen–Martio [18] and Kinnunen–Martio [20], where it is”
Cheeger-harmonic functions in metric measure spaces revisited (2013, unknown): “For a domainΩ ⊂ X, following [19], we define the Sobolev space with zero boundary values H(1,2) 0 (Ω) to be the space of those u ∈ H 1,2(X) for which uχX\Ω vanishes except a set of 2-capacity zero.”
The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values (2006, methodology): “These results are based on the definition of the first order Sobolev spaces with zero boundary values in metric spaces equipped with a Borel regular measure by Kilpelainen, Kinnunen, and Martio [ 25 ].”
Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces☆ (2003, background): “We follow [18] and define for a domain Ω the “Newtonian space with zero boundary values”, N 0 (Ω), to be the class of those Newtonian functions u for which uχX\Ω vanishes p-quasieverywhere.”