3 papers
math.AP2026
The Bifurcation Phenomenon for the Regularized Two-Phase Problem Associated with the -Laplacian
Alaa Haj Ali, Catherine Lebiedzik, Peiyong Wang
In this paper, we verify a bifurcation phenomenon regarding the multiplicity of weak solutions, subject to the Dirichlet boundary condition, of a regularized two-phase free boundar…
math.AP2026
Pointwise mean-value formulas with quantitative remainder for higher-order Poisson equations
Fernando Charro, Sophia Hertrich, Catherine Lebiedzik
Higher-order Poisson equations involve an integer power of the Laplacian and a nonzero forcing term, and appear in areas of physics and engineering such as hydrodynamics, structura…
math.AP2026
On the characterization of polyharmonic functions through iterated means
Fernando Charro, Catherine Lebiedzik, Md Nurul Raihen
We introduce an infinite family of mean-value formulas (exact and asymptotic) given in terms of linear combinations of iterated means. We prove that the mean-value formulas in this…