By Guidotti P.
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Extra info for A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems
1. It is natural to ask the question about maximal or global existence for the solution. A distinction need to be made between the two cases δ = 0 and δ > 0. 7) generically cross in ﬁnite time. It is not clear if any beneﬁt could come from the coupling to singular BVPs. In the second case it is possible to continue the solution to its maximal existence interval with the same technique used in the above existence proof. The question of global existence remains open. 2. The results concerning singular BVPs of Section 2 can be generalized to higher dimensions if the domain degeneration only occurs in one direction.
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A 2-D free boundary problem with onset of a phase and singular elliptic boundary value problems by Guidotti P.