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On the second eigenfunctions of the Laplacian in R2
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
inferredcites →https://doi.org/10.1002/9783527617210openalex-snapshot
Methods of Mathematical Physics
inferredcites →https://doi.org/10.1007/bf01221125openalex-snapshot
Symmetry and related properties via the maximum principle
inferredcites →https://doi.org/10.1090/s0002-9939-1988-0920985-9openalex-snapshot
A Counterexample to the Nodal Domain Conjecture and a Related Semilinear Equation
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
inferred← citeshttps://doi.org/10.2139/ssrn.4671773openalex-extracted
Nodal Lines of Eigenfunctions of Laplacian in Plane
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Convex domains with stationary hot spots
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On the “Hot Spots” Conjecture of J. Rauch
inferred← citeshttps://doi.org/10.1006/jfan.2000.3611openalex-snapshot
Sharp Inequalities for Heat Kernels of Schrödinger Operators and Applications to Spectral Gaps
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Geometric Structures of Laplacian Eigenfunctions
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Eigenfunctions and Harmonic Functions in Convex and Concave Domains
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Reflected Brownian Motion in Time Dependent Domains
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Probabilistic Proofs of Classical Theorems
inferred← citeshttps://doi.org/10.1007/978-3-319-04394-4_3openalex-snapshot
Overview of the “Hot Spots” Problem
inferred← citeshttps://doi.org/10.1007/978-3-319-04394-4_4openalex-snapshot
Neumann Eigenfunctions and Eigenvalues
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Synchronous and Mirror Couplings
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Parabolic Boundary Harnack Principle
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Neumann Heat Kernel Monotonicity
inferred← citeshttps://doi.org/10.1007/bf02564478openalex-snapshot
Nodal lines of eigenfunctions of the fixed membrane problem in general convex domains
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On the nodal lines of second eigenfunctions of the fixed membrane problem
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On the second eigenvalue of the dirichlet laplacian
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On Small Deviations of Gaussian Multiplicative Chaos with A Strictly Logarithmic Covariance on Euclidean Ball
inferred← citeshttps://doi.org/10.1016/j.aim.2021.107728openalex-snapshot
Morse index versus radial symmetry for fractional Dirichlet problems
inferred← citeshttps://doi.org/10.1016/j.cnsns.2021.105957openalex-snapshot
A counterexample to Payne’s nodal line conjecture with few holes
inferred← citeshttps://doi.org/10.1016/j.jde.2011.08.012openalex-snapshot
The nodal line of the second eigenfunction of the Robin Laplacian in R2 can be closed
inferred← citeshttps://doi.org/10.1016/j.jde.2012.06.002openalex-snapshot
Some results on the Schiffer conjecture in R2
inferred← citeshttps://doi.org/10.1016/j.jde.2026.114286openalex-snapshot
Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices
inferred← citeshttps://doi.org/10.1016/j.jfa.2022.109496openalex-snapshot
On the number of critical points of the second eigenfunction of the Laplacian in convex planar domains
inferred← citeshttps://doi.org/10.1016/j.jmaa.2021.125901openalex-snapshot
Optimal shapes for the first Dirichlet eigenvalue of the p-Laplacian and dihedral symmetry
inferred← citeshttps://doi.org/10.1016/j.matpur.2020.09.011openalex-snapshot
On nodal and generalized singular structures of Laplacian eigenfunctions and applications to inverse scattering problems
inferred← citeshttps://doi.org/10.1016/s0375-9601(01)00566-7openalex-snapshot
Classical and quantum-wedge billiards
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Asymptotic Analysis for the Lane–Emden Problem in Dimension Two
inferred← citeshttps://doi.org/10.1090/qam/1878259openalex-snapshot
Convex polyhedra quantum billiards in $\Bbb R^n$
inferred← citeshttps://doi.org/10.1090/s0033-569x-05-00975-3openalex-snapshot
Nodal and other properties of the second eigenfunction of the Laplacian in the plane
inferred← citeshttps://doi.org/10.1103/revmodphys.89.045005openalex-snapshot
Nodal portraits of quantum billiards: Domains, lines, and statistics
inferred← citeshttps://doi.org/10.1137/0524091openalex-snapshot
More Bounds on Eigenvalue Ratios for Dirichlet Laplacians in N Dimensions
inferred← citeshttps://doi.org/10.1214/21-ejp669openalex-snapshot
Tail bounds for gaps between eigenvalues of sparse random matrices
inferred← citeshttps://doi.org/10.1215/ijm/1258131110openalex-snapshot
On the second eigenvalue of the Laplacian in an annulus
inferred← citeshttps://doi.org/10.1512/iumj.2002.51.2208openalex-snapshot
Closed Nodal Lines and Interior Hot Spots of the Second Eigenfunctions of the Laplacian on Surfaces
inferred← citeshttps://doi.org/10.1512/iumj.2008.57.3170openalex-snapshot
Location of the nodal set for thin curved tubes
inferred← citeshttps://doi.org/10.1512/iumj.2009.58.3768openalex-snapshot
Minimization of $\lambda_{2}(\Omega)$ with a perimeter constraint
inferred← citeshttps://doi.org/10.1512/iumj.2013.62.4975openalex-snapshot
Closed nodal surfaces for simply connected domains in higher dimensions
inferred← citeshttps://doi.org/10.21248/gups.67965openalex-snapshot
Spectral characteristics of Dirichlet problems for nonlocal operators
inferred← citeshttps://doi.org/10.2139/ssrn.5955167openalex-snapshot
Mountain pass for the Ginzburg-Landau energy in a strip: solitons and solitonic vortices
inferred← citeshttps://doi.org/10.3233/asy-191594openalex-snapshot
On the multiplicity of the second eigenvalue of the Laplacian in non simply connected domains – with some numerics –
inferred← citeshttps://doi.org/10.3934/dcdss.2026196openalex-snapshot
Continuity of eigenfunctions of Kreĭn-Feller operators on Riemannian manifolds
inferred← citeshttps://doi.org/10.3934/era.2021080openalex-snapshot
On the number of critical points of solutions of semilinear elliptic equations
inferred← citeshttps://doi.org/10.4310/cag.1995.v3.n2.a3openalex-snapshot
On the multiplicity of the second eigenvalue of Laplacian in $R^2$
inferred← citeshttps://doi.org/10.4310/jdg/1214447811openalex-snapshot
On the nodal line of the second eigenfunction of the Laplacian in $\mathbf{R}^2$
inferred← citeshttps://doi.org/10.48550/arxiv.1009.4768openalex-snapshot
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
inferred← citeshttps://doi.org/10.48550/arxiv.1112.0207openalex-snapshot
Some Results on the Schiffer's Conjecture in R^2
inferred← citeshttps://doi.org/10.48550/arxiv.1411.0221openalex-snapshot
On the nodal line of a second eigenfunction of the Laplacian-Dirichlet in some annular domains with dihedral symmetry
inferred← citeshttps://doi.org/10.48550/arxiv.math/0009153openalex-snapshot
Closed nodal lines and interior hot spots of the second eigenfunction of the Laplacian on surfaces
inferred← citeshttps://doi.org/10.57262/die/1356019038openalex-snapshot
Maximum and antimaximum principles near the second eigenvalue
inferred← citeshttps://doi.org/10.5802/afst.1585openalex-snapshot
On the Nodal set of a second Dirichlet eigenfunction in a doubly connected domain
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Level sets of certain Neumann eigenfunctions under deformation of Lipschitz domains \\\\ Application to the Extended Courant Property
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