Harmonic functions on metric spaces

By Nageswari Shanmugalingam. 2001

249 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/dbccb52ff85a137c64b0b9bd7d9c439315aad030

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In Applied Mathematics

1. Anders Bjorn
2. P. Hajłasz
3. S. Keith
4. Jana Björn
5. Pekka Koskela
6. P. Hasto
7. Petteri Harjulehto
8. Heli Tuominen

In Mathematical Physics

1. Anders Bjorn
2. P. Hajłasz
3. Jana Björn
4. Pekka Koskela
5. Juha Kinnunen
6. P. Hasto
7. S. Keith
8. Petteri Harjulehto

Citations in the corpus

• Moser iteration for (quasi)minimizers on metric spaces (2006, background): “Let us explain the dicult y: In the proof of Theorem 4.8 in Shanmugalingam [ 41 ] she rst proves Lemma 4.10, and this later proof carries over verbatim to the noncomplete case.”
• ABSOLUTELY MINIMIZING LIPSCHITZ EXTENSIONS ON A METRIC SPACE (2002, background): “[11], and hence one might be able to base a general existence result on the same idea.”
• The Perron method for p-harmonic functions in metric spaces (2003, background): “6 in Shanmugalingam [35], see also Cheeger [8] and Heinonen–Kilpeläinen–Martio [12].”
• Regularity of quasi-minimizers on metric spaces (2001, methodology): “The norm is unambiguously defined by [ Sh1 ] and the obtained space is a Banach space.”
• Modulus and the Poincaré inequality on metric measure spaces (2003, background): “This has been extensively studied, see [HKM93,HK95a,HK96,HK98,HK99,BMS01,HST01, Sha01 , HKST01,KST01,Kei02].”
• Sobolev classes of Banach space-valued functions and quasiconformal mappings (2001, methodology): “It follows that without loss of generality we may assume that u E NI'Q(Y) with compact support, and that the Q-Poincar6 inequality holds in all of Y. Thus, u can be approximated in NI'Q(Y) by L*ipschitz functions with supports in a fixed compact set [ 47, Theorem 4.8 ].”
• The Dirichlet Energy Integral and Variable Exponent Sobolev Spaces with Zero Boundary Values (2006, methodology): “Here we use the same methods as in [ 37 ] to prove that a minimizer exists.”
• A weak Kellogg property for quasiminimizers (2006, unknown): “8 in Shanmugalingam [27], there is f ∈ Lipc( ′) such that ‖f − φ‖N1,p(X) < ε.”
• Space of Ricci Flows I (2009, background): “em 7.14 of Cheeger’s work [13], where a much more general case was considered. The weak maximum principle follows from the uniqueness. Also, the weak maximum principle was proved by Shanmugalligam in [78]. The strong maximum principle follows from Corollary 6.4 of [56]. However, we shall give a simp”
• Measure density and extendability of Sobolev functions (2008, background): “For the p-modulus on metric measure spaces and the properties of upper gradients, see for example [7], [13], [24], and [25].”
• Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology (2012, methodology): “Thus, the Dirichlet problem studied by Shanmugalingam [37] differs in general from the Dirichlet problem considered here.”