On some unexpected properties of radial and symmetric eigenvalues and eigenfunctions of the p-Laplacian on a disk

We discuss several properties of eigenvalues and eigenfunctions of the p-Laplacian on a ball subject to zero Dirichlet boundary conditions. Among main results, in two dimensions, we show the existence of nonradial eigenfunctions which correspond to the radial eigenvalues. Also we prove the existence...

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Vydáno v:Journal of Differential Equations Ročník 263; číslo 3; s. 1755 - 1772
Hlavní autoři: Bobkov, Vladimir, Drábek, Pavel
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 05.08.2017
Témata:
Cheeger constant
Cheeger set
Dirichlet p-Laplacian
Eigenvalue problem
Variational characterization of eigenvalues
47J10
Dirichlet p-Laplacian
35P15
49R05
Variational characterization of eigenvalues
Cheeger constant
Cheeger set
Eigenvalue problem
35P30
ISSN:0022-0396, 1090-2732
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Popis
Shrnutí:We discuss several properties of eigenvalues and eigenfunctions of the p-Laplacian on a ball subject to zero Dirichlet boundary conditions. Among main results, in two dimensions, we show the existence of nonradial eigenfunctions which correspond to the radial eigenvalues. Also we prove the existence of eigenfunctions whose shape of the nodal set cannot occur in the linear case p=2. Moreover, the limit behavior of some eigenvalues as p→1+ and p→+∞ is studied.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2017.03.028