Nonlinear potential theory on metric spaces

By Tero Mäkäläinen. 2008

441 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0870e99e24665918e840072c96314966fdae8f3c

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Citations in the corpus

Gradient estimates for heat kernels and harmonic functions (2017, background): “The proof uses a telescopic argument, which is by now classical; see for instance [60] and the monographs [19, 63].”
Yau's gradient estimates on Alexandrov spaces (2010, background): “Notice that the converse i s not true in general metric measure space (see [16]).”
Obstacle and Dirichlet problems on arbitrary nonopen sets in metric spaces, and fine topology (2012, methodology): “In metric spaces the single obstacle problem was studied by Kinnunen–Martio [26], while the double obstacle problem was studied by Farnana [16].”
Prime ends for domains in metric spaces (2012, background): “32 in Björn–Björn [10] we have an explicit estimate L ≤ 192C(3) μCPI.”
Nonsmooth differential geometry - An approach tailored for spaces with Ricci curvature bounded from below (2014, background): “1 in [20]) and the locality of the differential we deduce that the module span of dfn,1, .”
An Overview of the Proof of the Splitting Theorem in Spaces with Non-Negative Ricci Curvature (2014, background): “1 of [11] which gives a Lusin’s type approximation under this further assumptions):”
The Poincare inequality is an open ended condition (2008, methodology): “[32] J. Kinnunen and O. Martio, Nonlinear potential theory on metric spaces, Illinois J. Math.”
The abstract Lewy-Stampacchia inequality and applications (2014, background): “Key facts are that CD(K,N), N < ∞, spaces are doubling ([32]) and support a weak local 1-2 Poincaré inequality ([22], [28]) and a number of consequences about the behavior of harmonic functions can be deduced from these informations, see [8] for an overview on the subject.”
On the differential structure of metric measure spaces and applications (2012, background): “33) (6)in the context of non-linear potential theory the strong maximum principle for local sub/super-minimizers of the energy has been proved in [10].”
A weak Kellogg property for quasiminimizers (2006, background): “(a) ⇒ (c) This is Lemma 3.4 in Kinnunen–Martio [23] (after the observation in Remark 3.3 (4) above).”