Maximal solutions for the $\infty$-eigenvalue problem

DOI10.1515/ACV-2017-0024zbMATH Open1414.35077arXiv1704.01875OpenAlexW2724157631MaRDI QIDQ1739066

Author name not available (Why is that?)

Publication date: 24 April 2019

Published in: (Search for Journal in Brave)

Abstract: In this article we prove that the first eigenvalue of the

i n f t y -

Laplacian

left{ �egin{array}{rclcl} min{ -Delta_infty v,, |

abla v|-lambda_{1, infty}(Omega) v } & = & 0 & ext{in} & Omega v & = & 0 & ext{on} & partial Omega, end{array} ight. has a unique (up to scalar multiplication) maximal solution. This maximal solution can be obtained as the limit as $e l l e a r r o w 1$ of concave problems of the form left{ �egin{array}{rclcl} min{ -Delta_infty v_{ell},, |

abla v_{ell}|-lambda_{1, infty}(Omega) v_{ell}^{ell} } & = & 0 & ext{in} & Omega v_{ell} & = & 0 & ext{on} & partial Omega. end{array} ight.

In this way we obtain that the maximal eigenfunction is the unique one that is the limit of the concave problems as happens for the usual eigenvalue problem for the

p -

Laplacian for a fixed

1 < p < i n f t y

.

Full work available at URL: https://arxiv.org/abs/1704.01875

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Maximal solutions for the $\infty$-eigenvalue problem

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q1739066)

Maximal solutions for the \(\infty\)-eigenvalue problem