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Free boundary problems for the laplace equation: A priori estimates, existence theorems, asymptotic behaviours
Author(s) -
Dervieux A.,
Kawarada H.,
Fujita H.
Publication year - 1981
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/mma.1670030105
Subject(s) - mathematics , laplace's equation , domain (mathematical analysis) , boundary (topology) , free boundary problem , mathematical analysis , boundary value problem , laplace transform , obstacle , a priori and a posteriori , work (physics) , obstacle problem , a priori estimate , law , philosophy , epistemology , political science , mechanical engineering , engineering
This work is devoted to Free Boundary Problems with Laplace equation Δ u = f in the domain and the two conditions on the Free Boundary u = 1 and |grad u | = λ = const. In the model problems which we study, three cases arise: 1) f = 0, λ is given, 2) f = 0, λ is unknown and the length of the Free Boundary is given, 3) f ≠ 0, λ = 0 (Obstacle Problem).