Under a local L2 doubling condition, the nodal set of a solution to Δw = W·∇w + V w has (n−1)-dimensional Hausdorff measure bounded by a constant times a power of the Sobolev norms of W and V plus the doubling constant.
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Nodal set for the Schr\"odinger equation under a local growth condition
Under a local L2 doubling condition, the nodal set of a solution to Δw = W·∇w + V w has (n−1)-dimensional Hausdorff measure bounded by a constant times a power of the Sobolev norms of W and V plus the doubling constant.