Symmetry properties of stable solutions of semilinear elliptic equations in unbounded domains
| Autor: | Samuel Nordmann |
|---|---|
| Přispěvatelé: | Centre d'Analyse et de Mathématique sociales (CAMS), École des hautes études en sciences sociales (EHESS)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École des hautes études en sciences sociales (EHESS) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Neumann boundary conditions
Pure mathematics Semilinear elliptic equations 01 natural sciences Domain (mathematical analysis) Symmetry Mathematics - Analysis of PDEs Generalized principal eigenvalue Generalized principal Neumann boundary condition FOS: Mathematics Liouville property [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Mathematics Conjecture Applied Mathematics 010102 general mathematics Regular polygon 010101 applied mathematics Unbounded domains Elliptic curve Bounded function Homogeneous space De Giorgi's conjecture Convex domains Constant (mathematics) Stability Analysis Analysis of PDEs (math.AP) |
| Zdroj: | Calculus of Variations and Partial Differential Equations Calculus of Variations and Partial Differential Equations, Springer Verlag, In press |
| ISSN: | 0944-2669 1432-0835 |
| Popis: | We consider stable solutions of a semilinear elliptic equation with homogeneous Neumann boundary conditions. A classical result of Casten, Holland and Matano states that all stable solutions are constant in convex bounded domains. In this paper, we examine whether this result extends to unbounded convex domains. We give a positive answer for stable non-degenerate solutions, and for stable solutions if the domain $$\Omega $$ further satisfies $$\Omega \cap \{\vert x\vert \le R\}= O(R^2)$$ , when $$R\rightarrow +\infty $$ . If the domain is a straight cylinder, an additional natural assumption is needed. These results can be seen as an extension to more general domains of some results on De Giorgi’s conjecture. As an application, we establish asymptotic symmetries for stable solutions when the domain satisfies a geometric property asymptotically. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink