Free boundary problems for the laplace equation: A priori estimates, existence theorems, asymptotic behaviours | Zendy

Dervieux A. | Zendy; Kawarada H. | Zendy; Fujita H. | Zendy

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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) , free boundary problem , boundary (topology) , mathematical analysis , boundary value problem , laplace transform , obstacle , work (physics) , obstacle problem , a priori and a posteriori , law , mechanical engineering , philosophy , epistemology , political science , 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).

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