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math.AP2026
Sharp spectral estimates for free boundary problems arising in plasma physics
Daniele Bartolucci, Aleks Jevnikar, Juncheng Wei +1
We derive a sharp spectral estimate for a superlinear free boundary problem arising in plasma physics. The semilinear equation is coupled with a constraint, which forces the analys…
math.AP2024
Existence of Solutions to a super-Liouville equation with Boundary Conditions
Mingyang Han, Ruijun Wu, Chunqin Zhou
In this paper, we study the existence of solutions to a type of super-Liouville equation on the compact Riemannian surface with boundary and with its Euler characteristic $χ(M)…
math.AP2023
On the nodal set of solutions to Dirac equations
William Borrelli, Ruijun Wu
Motivated by various geometric problems, we study the nodal set of solutions to Dirac equations on manifolds, of general form. We prove that such set has Hausdorff dimension less t…