On the convexity and symmetry of solutions to an elliptic free boundary problem
1987 ◽
Vol 42
(1)
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pp. 57-68
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Keyword(s):
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.
Keyword(s):
2009 ◽
Vol 41
(1)
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pp. 391-414
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Keyword(s):
2016 ◽
Vol 18
(03)
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pp. 1650010
2016 ◽
Vol 260
(7)
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pp. 5875-5893
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Stationary solutions of a free boundary problem modeling growth of angiogenesis tumor with inhibitor
2018 ◽
Vol 23
(6)
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pp. 2593-2605
2021 ◽
Vol 26
(1)
◽
pp. 667-691
2009 ◽
Vol 246
(5)
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pp. 1845-1882
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