Local Monotonicity and Full Stability for Parametric Variational Systems

2016 ◽  
Vol 26 (2) ◽  
pp. 1032-1059 ◽  
Author(s):  
B. S. Mordukhovich ◽  
T. T. A. Nghia
Keyword(s):  
Local Monotonicity ◽  
Parametric Variational Systems ◽  
Variational Systems

scholarly journals Stability analysis of parametric variational systems

2011 ◽  
Vol 1 (2) ◽  
pp. 317-331 ◽  
Author(s):  
Shengji Li ◽  
◽  
Chunmei Liao ◽  
Minghua Li
Keyword(s):  
Stability Analysis ◽  
Parametric Variational Systems ◽  
Variational Systems

scholarly journals Full Stability of General Parametric Variational Systems

2018 ◽  
Vol 26 (4) ◽  
pp. 911-946 ◽  
Author(s):  
B. S. Mordukhovich ◽  
T. T. A. Nghia ◽  
D. T. Pham
Keyword(s):  
Parametric Variational Systems ◽  
Variational Systems

scholarly journals Metric regularity and Lipschitzian stability of parametric variational systems

2010 ◽  
Vol 72 (3-4) ◽  
pp. 1149-1170 ◽  
Author(s):  
Francisco J. Aragón Artacho ◽  
Boris S. Mordukhovich
Keyword(s):  
Metric Regularity ◽  
Lipschitzian Stability ◽  
Parametric Variational Systems ◽  
Variational Systems

scholarly journals Local Regularity for the Harmonic Map and Yang–Mills Heat Flows

2021 ◽  
Author(s):  
Ahmad Afuni
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Map ◽  
Local Regularity ◽  
Yang Mills ◽  
Heat Flows ◽  
Singular Sets ◽  
Regularity Results ◽  
Local Monotonicity ◽  
Partial Differ ◽  
Singular Time

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).

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