Critical points and level sets in exterior boundary problems

2009 ◽  
Vol 58 (4) ◽  
pp. 1947-1970 ◽  
Author(s):  
Alberto Enciso ◽  
Daniel Peralta-Salas
Keyword(s):  
Critical Points ◽  
Level Sets ◽  
Boundary Problems ◽  
Exterior Boundary

Fictitious domains and level sets for moving boundary problems. Applications to the numerical simulation of tumor growth

2011 ◽  
Vol 230 (4) ◽  
pp. 1335-1358 ◽  
Author(s):  
M. Carmen Calzada ◽  
Gema Camacho ◽  
Enrique Fernández-Cara ◽  
Mercedes Marín
Keyword(s):  
Numerical Simulation ◽  
Tumor Growth ◽  
Level Sets ◽  
Moving Boundary ◽  
Moving Boundary Problems ◽  
Boundary Problems

scholarly journals Oriented distance point of view on random sets

2020 ◽  
Vol 26 ◽  
pp. 84
Author(s):  
M. Dambrine ◽  
B. Puig
Keyword(s):  
Free Boundary ◽  
Level Sets ◽  
Free Boundary Problems ◽  
Point Of View ◽  
Random Sets ◽  
Boundary Problems ◽  
Open Set ◽  
Large Numbers ◽  
Oriented Distance ◽  
A Free Boundary Problem

Motivated by free boundary problems under uncertainties, we consider the oriented distance function as a way to define the expectation for a random compact or open set. In order to provide a law of large numbers and a central limit theorem for this notion of expectation, we also address the question of the convergence of the level sets of fn to the level sets of f when (fn) is a sequence of functions uniformly converging to f. We provide error estimates in term of Hausdorff convergence. We illustrate our results on a free boundary problem.

Singular critical points for variational free boundary problem from isoparametric hypersurfaces

2016 ◽  
Vol 18 (03) ◽  
pp. 1650010
Author(s):  
Lizhou Wang
Keyword(s):  
Free Boundary ◽  
Boundary Value Problem ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Critical Points ◽  
Unit Sphere ◽  
Level Sets ◽  
Isoparametric Hypersurfaces ◽  
Homogeneous Solutions ◽  
Overdetermined Boundary Value Problem

We construct three families of singular critical points for a variational free boundary problem. These critical points are homogeneous solutions of degree one to some overdetermined boundary value problem. The intersections of the level sets of these solutions with the unit sphere are isoparametric hypersurfaces and their focal submanifolds.

Solution of the Dirichlet and Stokes exterior boundary problems for the Earth's ellipsoid

2001 ◽  
Vol 74 (11-12) ◽  
pp. 767-772 ◽  
Author(s):  
V. V. Brovar ◽  
Z. S. Kopeikina ◽  
M. V. Pavlova
Keyword(s):  
Boundary Problems ◽  
Exterior Boundary

PRESCRIBING MEAN CURVATURE ON 𝔹n

2010 ◽  
Vol 21 (09) ◽  
pp. 1157-1187 ◽  
Author(s):  
WAEL ABDELHEDI ◽  
HICHEM CHTIOUI
Keyword(s):  
Critical Points ◽  
Mean Curvature ◽  
Level Sets ◽  
Curvature Function ◽  
Number Of Solutions ◽  
Total Contribution ◽  
Prescribed Mean Curvature ◽  
The Difference ◽  
Zero Scalar Curvature ◽  
Lagrange Functional

In this paper, we consider the problem of multiplicity of conformal metrics that are equivalent to the Euclidean metric, with zero scalar curvature and prescribed mean curvature on the boundary of the ball 𝔹n, n ≥ 4. Under the assumption that the order of flatness at critical points of the prescribed mean curvature function H(x) is β∈(n-2, n-1), we establish some Morse inequalities at infinity, which give a lower bound on the number of solutions to the above problem, in terms of the total contribution of its critical points at infinity to the difference of topology between the level sets of the associated Euler–Lagrange functional. As a by-product of our arguments, we derive a new existence result through an Euler–Hopf type formula.

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