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math.AP2025
A Lane-Emden system of free boundary type: existence, uniqueness and monotonicity of solutions
Daniele Bartolucci, Yeyao Hu, Aleks Jevnikar +2
We consider a Hamiltonian system of free boundary type, showing first uniform bounds and existence of solutions and of the free boundary. Then, for any smooth and bounded domain, w…
math.AP2025
Classification of singular limits for free boundary and singularly perturbed elliptic problems: the Dancer-Yan spikes revisited
Daniele Bartolucci, Aleks Jevnikar, Juncheng Wei +1
We classify the singular limits relative to a free boundary problem arising in plasma physics in dimension , under suitable natural integral bounds. It turns out that one of t…
math.AP2025
Symmetry in Serrin-type overdetermined problems
Daomin Cao, Juncheng Wei, Weicheng Zhan
This paper investigates the geometric constraints imposed on a domain by overdetermined problems for partial differential equations. Serrin's symmetry results are extended to overd…