Asymptotic Behavior of Free Boundaries at Their Singular Points

1977 ◽  
Vol 106 (2) ◽  
pp. 309 ◽  
Author(s):  
L. A. Caffarelli ◽  
N. M. Riviere
Keyword(s):  
Asymptotic Behavior ◽  
Singular Points ◽  
Free Boundaries

scholarly journals Asymptotic Behavior of the Hyperbolic Schwarz Map at Irregular Singular Points

2010 ◽  
Vol 53 (1) ◽  
pp. 99-132
Author(s):  
Tatsuya Koike ◽  
Takeshi Sasaki ◽  
Masaaki Yoshida
Keyword(s):  
Asymptotic Behavior ◽  
Singular Points ◽  
Irregular Singular Points

scholarly journals On the asymptotic behavior of the solutions to parabolic variational inequalities

2020 ◽  
Vol 2020 (768) ◽  
pp. 149-182
Author(s):  
Maria Colombo ◽  
Luca Spolaor ◽  
Bozhidar Velichkov
Keyword(s):  
Asymptotic Behavior ◽  
Variational Inequalities ◽  
Stationary Solution ◽  
Global Solutions ◽  
Singular Points ◽  
Obstacle Problems ◽  
Abstract Result ◽  
Łojasiewicz Inequality ◽  
Lojasiewicz Inequality ◽  
Thin Obstacle

AbstractWe consider various versions of the obstacle and thin-obstacle problems, we interpret them as variational inequalities, with non-smooth constraint, and prove that they satisfy a new constrained Łojasiewicz inequality. The difficulty lies in the fact that, since the constraint is non-analytic, the pioneering method of L. Simon ([22]) does not apply and we have to exploit a better understanding on the constraint itself. We then apply this inequality to two associated problems. First we combine it with an abstract result on parabolic variational inequalities, to prove the convergence at infinity of the strong global solutions to the parabolic obstacle and thin-obstacle problems to a unique stationary solution with a rate. Secondly, we give an abstract proof, based on a parabolic approach, of the epiperimetric inequality, which we then apply to the singular points of the obstacle and thin-obstacle problems.

Binary diagrams of mesomorphous compounds exhibiting singular points

1978 ◽  
Vol 3 ◽  
pp. 381-386 ◽  
Author(s):  
F. Hardouin ◽  
G. Sigaud ◽  
M.-F. Achard ◽  
H. Gasparoux
Keyword(s):  
Singular Points
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