3 papers
math.AP2026
Free Boundary Regularity for Non-Convex Fully Nonlinear Alt-Phillips Problems
Alvis Zahl
This paper studies the fully nonlinear Alt-Phillips free boundary problem \begin{equation} F(D^2u) = u^γχ_{\{u>0\}}, \end{equation} for without any convexity assump…
math.AP2025
Minimizing Eigenvalues of the Fractional Laplacian
Alvis Zahl
We study the minimizers of \begin{equation} λ_k^s(A) + |A| \end{equation} where is the -th Dirichlet eigenvalue of the fractional Laplacian on . Unlike in the case…
math.AP2021
First Order Hyperbolic Boundary Value Problems With a Large Oscillatory Zero Order Term
Alvis Zahl
We study the weakly stable hyperbolic boundary value problem with a large zero order oscillatory coefficient. This problem is related to linearized problems in the study of Mach st…