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Construction of signed distance functions through an elliptic equation

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arxiv 2401.17665 v2 pith:YKGIYSB6 submitted 2024-01-31 math.AP

Takahiro Hasebe , Jun Masamune , Tomoyuki Oka , Kota Sakai , Takayuki Yamada This is my paper · ORCID
classification math.AP
keywords distanceequationadvancesapproachappropriateasymptoticboundarybuilding
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Motivated by recent advances in structural optimization, we propose a novel method for constructing the distance function to the boundary of a given domain. Building on and extending the celebrated Varadhan asymptotic theory, our approach reformulates the governing equation into a more appropriate framework. A central contribution of this work is the derivation of convergence rates within this new setting, which are shown to be optimal in one dimension and offer significant improvements over existing results in higher dimensions.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations

    math.AP 2025-06 conditional novelty 8.0 of 10

    Vanishing viscosity for uniformly convex Hamilton-Jacobi equations converges at the optimal rate O(epsilon log epsilon), improving the old O(sqrt(epsilon)) bound.

  2. Short-time behavior and invariant surfaces for caloric functions with non-constant boundary values

    math.AP 2026-07 conditional novelty 6.0 of 10

    For heat equations with zero initial data and non-negative Dirichlet data, short-time exponential decay is governed by the distance to the set where the boundary data is positive.

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