Work

Modica-type estimates and curvature results for overdetermined elliptic problems

Year: 2024

Type: article

Abstract: In this paper, we establish a Modica-type estimate on bounded solutions to the overdetermined elliptic problem [Formula: see text] where [Formula: see text] [Formula: see text]. As we will see, the presence of the boundary changes the usual form of the Modica estimate for entire solutions. We will also discuss the equality case. From such estimates, we will deduce information about the curvature of [Formula: see text] under a certain condition on [Formula: see text] and [Formula: see text]. The proof uses the maximum principle together with scaling arguments and a careful passage to the limit in the arguments by contradiction.

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199724500500

Authors: David Ruiz, Pieralberto Sicbaldi, Jing Wu

Institutions: Universidad de Granada, Centre National de la Recherche Scientifique, Aix-Marseille Université, Institut de Mathématiques de Marseille, Centrale Méditerranée

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: China Scholarship Council, Ministerio de Ciencia e Innovación, Agencia Estatal de Investigación