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Yong Liu Kelei Wang Juncheng Wei 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2018,35(4):993-1017
From minimal surfaces such as Simons' cone and catenoids, using refined Lyapunov–Schmidt reduction method, we construct new solutions for a free boundary problem whose free boundary has two components. In dimension 8, using variational arguments, we also obtain solutions which are global minimizers of the corresponding energy functional. This shows that the theorem of Valdinoci et al. [41], [42] is optimal. 相似文献
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By introducing a partial order and using the Mönch fixed point theorem, we establish the existence of maximal and minimal solutions in Banach spaces to a boundary value problem for the equation of the bending of an elastic beam. 相似文献
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Well‐posedness of a parabolic free boundary problem driven by diffusion and surface tension 下载免费PDF全文
Martijn M. Zaal 《Mathematical Methods in the Applied Sciences》2015,38(2):380-392
Well‐posedness and regularity results are shown for a class of free boundary problems consisting of diffusion on a free domain where the boundary movement depends on its mean curvature of the boundary and the diffusion on the boundary, and initial conditions are radially symmetric. Short‐time existence and uniqueness of solutions in a suitable Sobolev space are shown using a fixed‐point argument. Higher regularity is a posteriori. Finally, it is shown that solutions exist globally in time and converge to equilibrium if the boundary movement depends on the mean curvature of the boundary and diffusion in a specific way. A mathematical model describing the swelling of a cell due to osmosis is treated as an example. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献