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math.AP2024
Structure of the free interfaces near triple junction singularities in harmonic maps and optimal partition problems
Roberto Ognibene, Bozhidar Velichkov
We consider energy-minimizing harmonic maps into trees and we prove the regularity of the singular part of the free interface near triple junction points. Precisely, by proving a n…
math.AP2024
On asymptotics of Robin eigenvalues in the Dirichlet limit
Roberto Ognibene
We investigate the asymptotic behavior of the eigenvalues of the Laplacian with homogeneous Robin boundary conditions, when the (positive) Robin parameter is diverging. In this fra…
math.AP2024
Boundary regularity of the free interface in spectral optimal partition problems
Roberto Ognibene, Bozhidar Velichkov
We consider the problem of optimal partition of a domain with respect to the sum of the principal eigenvalues and we prove for the first time regularity results for the free interf…