OpenAlex ·
The stability conjecture for the Bernoulli problem in dimension four
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.05669
- Original
- Read it at the publisher
- Topics
Abstract
We prove that every global classical stable solution to the one-phase Bernoulli problem in $\mathbb R^4$ is one-dimensional. In particular, if nonempty, its free boundary consists of one or two parallel hyperplanes. This settles the stability conjecture for the Bernoulli problem in dimension four. As consequences, we obtain universal local Hessian and free-boundary curvature estimates for classical stable solutions in $\mathbb R^4$, as well as axial symmetry of global classical solutions with finite Morse index in $\mathbb R^4$.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Materials Science
The convergent laboratory: when AI reasoning, autonomous experiments, high performance and quantum computing reshape chemistry
Human-agent discovery of reconfigurable in-plane ferroelectric superdomain control
Demonstration of room-temperature, magnetic-field-free, and ultralow-power spin-orbit torque logic device based on composition-uniform van der Waals magnet Fe3GaTe2
Online Surrogate Repair: Decoupling High-Fidelity Feedback from Search Length in Closed-Loop Discovery
Learning Metamaterial Eigenmodes with Wavelet-Encoded Fourier Neural Operators
Get the few papers worth your time in Materials Science every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.