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Communications in Partial Differential Equations Volume 39, 2014 - Issue 12
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Original Articles

Lower Bounds on Nodal Sets of Eigenfunctions via the Heat Flow

Stefan Steinerberger Department of Mathematics, Yale University, New Haven, Connecticut, USACorrespondence[email protected]
Pages 2240-2261 | Received 03 May 2013, Accepted 07 Jun 2014, Published online: 16 Sep 2014

Citations (19)

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Read on this site (3)

Bogdan Georgiev & Mayukh Mukherjee. (2022) Some applications of heat flow to Laplace eigenfunctions. Communications in Partial Differential Equations 47:4, pages 677-700.
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Stefan Steinerberger. (2021) Regularized potentials of Schrödinger operators and a local landscape function. Communications in Partial Differential Equations 46:7, pages 1262-1279.
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Janna Lierl & Stefan Steinerberger. (2018) A local Faber–Krahn inequality and applications to Schrödinger equations. Communications in Partial Differential Equations 43:1, pages 66-81.
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Articles from other publishers (16)

Jiuyi Zhu. (2022) Boundary Doubling Inequality and Nodal sets of Robin and Neumann eigenfunctions. Potential Analysis 59:1, pages 375-407.
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Fanghua Lin & Jiuyi Zhu. (2020) Upper bounds of nodal sets for eigenfunctions of eigenvalue problems. Mathematische Annalen 382:3-4, pages 1957-1984.
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Fabio Cavalletti & Sara Farinelli. (2021) Indeterminacy estimates and the size of nodal sets in singular spaces. Advances in Mathematics 389, pages 107919.
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Stefan Steinerberger. (2020) On Sublevel Set Estimates and the Laplacian. Potential Analysis 55:1, pages 11-28.
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Jiuyi Zhu. (2020) Geometry and interior nodal sets of Steklov eigenfunctions. Calculus of Variations and Partial Differential Equations 59:5.
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Stefan Steinerberger. (2019) An Endpoint Alexandrov Bakelman Pucci Estimate in the Plane. Canadian Mathematical Bulletin 62:3, pages 643-651.
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Bogdan Georgiev & Mayukh Mukherjee. (2019) Some remarks on nodal geometry in the smooth setting. Calculus of Variations and Partial Differential Equations 58:3.
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Jiuyi Zhu. (2019) Doubling Inequality and Nodal Sets for Solutions of Bi-Laplace Equations. Archive for Rational Mechanics and Analysis 232:3, pages 1543-1595.
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Xiuyuan Cheng, Manas Rachh & Stefan Steinerberger. (2019) On the diffusion geometry of graph Laplacians and applications. Applied and Computational Harmonic Analysis 46:3, pages 674-688.
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Manas Rachh & Stefan Steinerberger. (2018) On the Location of Maxima of Solutions of Schrödinger's Equation. Communications on Pure and Applied Mathematics 71:6, pages 1109-1122.
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Hamid Hezari. (2018) Applications of small-scale quantum ergodicity in nodal sets. Analysis & PDE 11:4, pages 855-871.
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Bogdan Georgiev & Mayukh Mukherjee. (2018) Nodal geometry, heat diffusion and Brownian motion. Analysis & PDE 11:1, pages 133-148.
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Anup Biswas. (2017) Location of Maximizers of Eigenfunctions of Fractional Schrödinger’s Equations. Mathematical Physics, Analysis and Geometry 20:4.
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Jianfeng Lu & Stefan Steinerberger. (2017) A variation on the Donsker–Varadhan inequality for the principal eigenvalue. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473:2204, pages 20160877.
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Stefan Steinerberger. (2017) Localization of quantum states and landscape functions. Proceedings of the American Mathematical Society 145:7, pages 2895-2907.
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Florian Pausinger & Stefan Steinerberger. (2015) On the distribution of local extrema in Quantum Chaos. Physics Letters A 379:6, pages 535-541.
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