Journal of the Mathematical Society of Japan· 2026Q2
Construction of signed distance functions through an elliptic equation
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- Q2SCImago
- 2026year
Short summary
A novel method constructs signed distance functions using an elliptic equation, extending Varadhan's theory and achieving optimal convergence rates in 1D and improved rates in higher dimensions.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proposes a novel method for constructing signed distance functions to domain boundaries.
- Extends Varadhan's asymptotic theory to a new framework for this problem.
- Derives convergence rates for the new method.
- Achieves optimal convergence rates in 1D and improved rates in higher dimensions.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Journal of the Mathematical Society of Japan, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics