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.

scholarly journals Sign-changing two-peak solutions for an elliptic free boundary problem related to confined plasmas

2018 ◽  
Vol 7 (3) ◽  
pp. 385-405 ◽  
Author(s):  
Giovanni Pisante ◽  
Tonia Ricciardi
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Level Sets ◽  
Type Problem ◽  
Qualitative Properties ◽  
Confined Plasmas

AbstractBy a perturbative argument, we construct solutions for a plasma-type problem with two opposite-signed sharp peaks at levels 1 and {-\gamma}, respectively, where {0<\gamma<1}. We establish some physically relevant qualitative properties for such solutions, including the connectedness of the level sets and the asymptotic location of the peaks as {\gamma\to 0^{+}}.

scholarly journals On the convexity and symmetry of solutions to an elliptic free boundary problem

1987 ◽  
Vol 42 (1) ◽  
pp. 57-68 ◽  
Author(s):  
Bernhard Kawohl
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Level Sets ◽  
Stationary Solutions ◽  
Diffusion Reaction ◽  
Regularity Of Solutions ◽  
Symmetry Properties ◽  
Neumann Type ◽  
Type Boundary

AbstractWe study the existence, uniqueness and regularity of solutions to an exterior elliptic free boundary problem. The solutions model stationary solutions to nonlinear diffusion reaction problems, that is, they have compact support and satisfy both homogeneous Dirichlet and Neumann-type boundary conditions on the free boundary ∂{u > 0}. Then we prove convexity and symmetry properties of the free boundary and of the level sets {u > c} of the solutions. We also establish symmetry properties for the corresponding interior free boundary problem.

scholarly journals Higher Critical Points in an Elliptic Free Boundary Problem

2017 ◽  
Vol 28 (2) ◽  
pp. 1258-1294 ◽  
Author(s):  
David Jerison ◽  
Kanishka Perera
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Critical Points

Uniqueness of solution to a free boundary problem from combustion with transport

MAT Serie A ◽  
2001 ◽  
Vol 5 ◽  
pp. 37-41
Author(s):  
Claudia Lederman ◽  
Juan Luis Vázquez ◽  
Noemí Wolanski
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Uniqueness Of Solution ◽  
A Free Boundary Problem
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