Fetching the paper…
Reading the bibliography…
The Hot Spots constant for bounded smooth domains was recently introduced by Steinerberger (2021) as a means to control the global extrema of the first nontrivial eigenfunction of the Neumann Laplacian by its boundary extrema.
Remarks on Courant’s nodal line theorem
Å. Pleijel · 1956
Earlier work this paper cites.
On the construction of two-dimensional diffusion processes satisfying Wentzell’s boundary conditions and its application to boundary value problems
N. Ikeda · 1960
Earlier work this paper cites.
A construction of reflecting barrier Brownian motions for bounded domains
M. Fukushima · 1967
Earlier work this paper cites.
The probability distribution of the solution of the problem with an oblique derivative
A. P. Korostelev · 1973
Earlier work this paper cites.
Five problems: an introduction to the qualitative theory of partial differential equations
J. Rauch · 1975
Earlier work this paper cites.
A probabilistic solution of the Neumann problem
G. A. Brosamler · 1976
Earlier work this paper cites.
Rearrangements and convexity of level sets in PDE
B. Kawohl · 1985
Earlier work this paper cites.
Some potential theory for reflecting Brownian motion in Hölder and Lipschitz domains
R. F. Bass and P. Hsu · 1991
Earlier work this paper cites.
The essential spectrum of Neumann Laplacians on some bounded singular domains
R. Hempel, L. A. Seco, and B. Simon · 1991
Earlier work this paper cites.
Some inequalities for the first positive zeros of Bessel functions
L. Lorch · 1993
Earlier work this paper cites.
Bounds and monotonicities for the zeros of derivatives of ultraspherical Bessel functions
L. Lorch and P. Szego · 1994
Earlier work this paper cites.
Probabilistic techniques in analysis
R. F. Bass · 1995
Earlier work this paper cites.
Brownian motion, obstacles and random media
A.-S. Sznitman · 1998
Earlier work this paper cites.
On the “hot spots” conjecture of J. Rauch
R. Bañuelos and K. Burdzy · 1999
Cited alongside, same era.
A counterexample to the “hot spots” conjecture
K. Burdzy and W. Werner · 1999
Cited alongside, same era.
Fiber Brownian motion and the “hot spots” problem
R. F. Bass and K. Burdzy · 2000
Cited alongside, same era.
The “hot spots” conjecture for domains with two axes of symmetry
D. Jerison and N. Nadirashvili · 2000
Cited alongside, same era.
Probabilistic approaches to eigenvalue problems
M. N. Pascu · 2001
Cited alongside, same era.
Reflecting Brownian motion in a Lipschitz domain and a conditional gauge theorem
S. Ramasubramanian · 2001
Cited alongside, same era.
Exit problems associated with affine reflection groups
Y. Doumerc and J. Moriarty · 2009
Later among the works it cites.
Regularity of solutions of linear second order elliptic and parabolic boundary value problems on Lipschitz domains
R. Nittka · 2011
Later among the works it cites.
Hot spots conjecture for a class of acute triangles
B. Siudeja · 2015
Later among the works it cites.
Shape optimization and spectral theory
A. Henrot, editor · 2017
Later among the works it cites.
Torsional rigidity for cylinders with a Brownian fracture
M. van den Berg and F. den Hollander · 2018
Later among the works it cites.
L ∞ L_{\infty} -estimates for the torsion function and L ∞ L_{\infty} -growth of semigroups satisfying Gaussian bounds
H. Vogt · 2019
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Scaling coupling of reflecting Brownian motions and the hot spots problem
M. N. Pascu · 2002
Cited alongside, same era.
On Neumann eigenfunctions in lip domains
R. Atar and K. Burdzy · 2004
Cited alongside, same era.
Brownian motion with killing and reflection and the “hot-spots” problem
R. Bañuelos, M. Pang, and M. Pascu · 2004
Cited alongside, same era.
On an inequality for the eigenvalues of the Dirichlet and Neumann problems for the Laplace operator
N. Filonov · 2004
Cited alongside, same era.
The hot spots problem in planar domains with one hole
K. Burdzy · 2005
Cited alongside, same era.
Extremum problems for eigenvalues of elliptic operators
A. Henrot · 2006
Cited alongside, same era.
Bounds for exit times of brownian motion and the first dirichlet eigenvalue for the laplacian
R. Bañuelos, P. Mariano, and J. Wang · 2020
Later among the works it cites.
Euclidean triangles have no hot spots
C. Judge and S. Mondal · 2020
Later among the works it cites.
Conformal Skorokhod embeddings and related extremal problems
P. Mariano and H. Panzo · 2020
Later among the works it cites.
The hot spots conjecture can be false: Some numerical examples
A. Kleefeld · 2021
Closest in time.
Spectral upper bound for the torsion function of symmetric stable processes
H. Panzo · 2021
Closest in time.
An upper bound on the Hot Spots constant
S. Steinerberger · 2021
Closest in time.