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@INPROCEEDINGS{Kleefeld:891450,
      author       = {Kleefeld, Andreas},
      title        = {{T}he hot spots conjecture can be false: {S}ome numerical
                      examples using boundary integral equations},
      school       = {University of Lafayette},
      reportid     = {FZJ-2021-01532},
      year         = {2021},
      abstract     = {The hot spots conjecture is only known to be true for
                      special geometries. It can be shown numerically that the hot
                      spots conjecture can fail to be true for easy to construct
                      bounded domains with one hole. The underlying eigenvalue
                      problem for the Laplace equation with Neumann boundary
                      condition is solved with boundary integral equations
                      yielding a non-linear eigenvalue problem. Its discretization
                      via the boundary element collocation method in combination
                      with the algorithm by Beyn yields highly accurate results
                      both for the first non-zero eigenvalue and its corresponding
                      eigenfunction which is due to superconvergence. Finally,
                      numerical examples for easy to construct domains with up to
                      five holes are provided which fail the hot spots conjecture
                      as well.},
      organization  = {UL Virtual Colloquium, (USA)},
      subtyp        = {Invited},
      cin          = {JSC},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Enabling Computational- $\&$ Data-Intensive Science
                      and Engineering (POF4-511)},
      pid          = {G:(DE-HGF)POF4-511},
      typ          = {PUB:(DE-HGF)31},
      url          = {https://juser.fz-juelich.de/record/891450},
}