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).
Br¨ uning, ¨Uber Knoten von Eigenfunktionen des Laplace-Beltrami Operators, Mathematische Zeitschrift, 1978, 158: 15-21
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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).