arXiv Open Access 2015

Characterization of stadium-like domains via boundary value problems for the infinity Laplacian

Graziano Crasta Ilaria Fragalà

Lihat Sumber

Abstrak

We give a complete characterization, as "stadium-like domains", of convex subsets $Ω$ of $\mathbb{R}^n$ where a solution exists to Serrin-type overdetermined boundary value problems in which the operator is either the infinity Laplacian or its normalized version. In case of the not-normalized operator, our results extend those obtained in a previous work, where the problem was solved under some geometrical restrictions on $Ω$. In case of the normalized operator, we also show that stadium-like domains are precisely the unique convex sets in $\mathbb{R}^n$ where the solution to a Dirichlet problem is of class $C^{1,1} (Ω)$.

Topik & Kata Kunci

math.AP

Penulis (2)

Graziano Crasta

Ilaria Fragalà

Format Sitasi

APA MLA BibTeX

Crasta, G., Fragalà, I. (2015). Characterization of stadium-like domains via boundary value problems for the infinity Laplacian. https://arxiv.org/abs/1509.01681

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2015
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓