Upper bound on (n-1)-Hausdorff measure of nodal sets for the Dirichlet problem Δu + V u = 0 with analytic V is C(1 + log(‖∇V‖_∞ + 1)) ⋅ (‖V‖_∞^{1/2} + ‖∇V‖_∞^{1/2} + 1).
Ariturk, Lower bounds for nodal sets of Dirichlet and N eumann eigenfunctions, Communications in Mathe- matical Physics, 2013, 317(3): 817-825
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Measure upper bounds of nodal sets of solutions to Dirichlet problem of Schr\"{o}dinger equations
Upper bound on (n-1)-Hausdorff measure of nodal sets for the Dirichlet problem Δu + V u = 0 with analytic V is C(1 + log(‖∇V‖_∞ + 1)) ⋅ (‖V‖_∞^{1/2} + ‖∇V‖_∞^{1/2} + 1).