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On a Free Boundary Problem
Author(s) -
Boucherif Abdelkader,
Bouguima Sidi Mohammed
Publication year - 1996
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/(sici)1099-1476(199610)19:15<1257::aid-mma834>3.0.co;2-t
Subject(s) - heaviside step function , mathematics , omega , ball (mathematics) , boundary (topology) , mathematical analysis , unit sphere , boundary value problem , free boundary problem , combinatorics , pure mathematics , mathematical physics , physics , quantum mechanics
This paper considers a discontinuous semilinear elliptic problem: \[‐\Delta u=g(u)H(u‐\mu )\quad \text{in }\Omega,\qquad u=h\quad \text{on }%\partial \Omega,\] −Δ u = g ( u ) H ( u −μ) in Ω, u = h on ∂Ω, where H is the Heaviside function, μ a real parameter and Ω the unit ball in ℝ 2 . We deal with the existence of solutions under suitable conditions on g, h , and μ. It is shown that the free boundary, i.e. the set where u =μ, is sufficiently smooth.