Regularity of quasi-minimizers on metric spaces
By Juha Kinnunen, Nageswari Shanmugalingam. 2001
247 citations recorded by the source corpus.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/053a6e3c7f68934f2e4ee3d2c952bdf7a0575507
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In Applied Mathematics
- Anders Bjorn
- Pekka Koskela
- Renjin Jiang
- Boumediene Abdellaoui
- T. Coulhon
- S. Keith
- Hui-Chun Zhang
- A. Primo
In Computational Theory and Mathematics
- Boumediene Abdellaoui
- A. Primo
- I. Peral
- María Medina
- Anders Bjorn
- Tuomo Kuusi
- Matteo Cozzi
- N. Marola
Citations in the corpus
- Moser iteration for (quasi)minimizers on metric spaces (2006, methodology): “Note that in Kinnunen–Shanmugalingam [31], Section 2.”
- Regularity results and Harnack inequalities for minimizers and solutions of nonlocal problems: A unified approach via fractional De Giorgi classes (2016, background): “We present it here in a version with balls in place of cubes, due to [41].”
- The Poincare inequality is an open ended condition (2008, methodology): “[2] J. Björn, P. MacManus, and N. Shanmugalingam, Fat sets and pointwise boundary estimates for p-harmonic functions in metric spaces, J. Anal.”
- Lipschitz continuity of Cheeger-harmonic functions in metric measure spaces☆ (2003, background): “Thus Cheeger-harmonic functions are quasiminimizers in the sense of [19].”
- Harnack inequality and hyperbolicity for subelliptic p-Laplacians with applications to Picard type theorems (2001, methodology): “Such inequalities have already been proved in many settings: for a class of elliptic operators generalizing the ordinary p-Laplace operator in the Euclidean space (see the forerunner papers [71], for p = 2, then [93] and [100] for general p, and the book [42] for an up-to-date exposition), in [10] f”
- The effect of the Hardy potential in some Calder\'on-Zygmund properties for the fractional Laplacian (2015, background): “ to (21).Then, there exists a constant η∈ (0,1) depending only on N, sand γsuch that 1 |Br|dµ Z Br vηdµ 1 η 6 Cinf Br v. EFFECT OF THE HARDY POTENTIAL ON THE SUMMABILITY 17 To prove Lemma 3.7 (see [26] and [16, Lemma 4.1]) we need the next covering result in the spirit of Krylov-Safonov theory. Not”
- Harnack estimates for weak supersolutions to nonlinear degenerate parabolic equations (2008, unknown): “The proof follows [19].”