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arXiv · 2507.19600

Nodal set for the Schr\"odinger equation under a local growth condition

Igor Kukavica·Linfeng Li
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Abstract

We address the upper bound on the size of the nodal set for a solution $w$ of the Schr\"odinger equation $\Delta w= W\cdot \nabla w+V w$ in an open set in $\mathbb{R}^n$, where the coefficients belong to certain Sobolev spaces. Assuming a local doubling condition for the solution $w$, we establish an upper bound on the $(n-1)$-dimensional Hausdorff measure of the nodal set, with the bound depending algebraically on the Sobolev norms of $W$ and $V$.

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Igor Kukavica, Linfeng Li. 2025-07-25. Nodal set for the Schr\"odinger equation under a local growth condition. https://arxiv.org/abs/2507.19600

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