Directional ellipticity on special domains: weak Maximum and Phragmèn-Lindelöf principles

2019/02/04 by Italo Capuzzo Dolcetta, Dolcetta, Italo Capuzzo, Antonio Vitolo +1
Computer Science · Mathematics · #35B50 #35B53 #35D40 #35J60 #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1902.01296

openalex publication_date 2019/02/04 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

We prove the validity of maximum principles for a class of fully nonlinear operators on unbounded subdomains Ω⊂ \mathbb Rⁿ of cylindrical type. The main structural assumption is the uniform ellipticity of the operator along the bounded directions of Ω, with possible degeneracy along the unbounded directions.

Related

• Large sets at infinity and Maximum Principle on unbounded domains for a\n class of sub-elliptic operators
• On the maximum principle for general linear elliptic equations
• Maximum principles in unbounded Riemannian domains
• New maximum principles for linear elliptic equations
• Phragmén--Lindelöf theorems for a weakly elliptic equation with a nonlinear dynamical boundary condition