Sharp Liouville Theorems

Autor: Villegas Salvador

Publikováno v: Advanced Nonlinear Studies, Vol 21, Iss 1, Pp 95-105 (2021)

Consider the equation div⁡(φ2⁢∇⁡σ)=0{\operatorname{div}(\varphi^{2}\nabla\sigma)=0} in ℝN{\mathbb{R}^{N}}, where φ>0{\varphi>0}. Berestycki, Caffarelli and Nirenberg proved in [H. Berestycki, L. Caffarelli and L. Nirenberg, Further quali

Externí odkaz: https://doaj.org/article/c5ad475d3fe745de8bef02db17ba1223

Non-existence of patterns and gradient estimates

Autor: Nordmann, Samuel

We call pattern any non-constant stable solution of a semilinear elliptic equation with Neumann boundary conditions. A classical theorem of Casten, Holland [19] and Matano [49] states that stable patterns do not exist in convex domains. In this artic

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::03251cc382083e835047d7b9bb77b12e
https://hal.archives-ouvertes.fr/hal-02539365/file/Stable-curvature2.pdf

Symmetry properties of stable solutions of semilinear elliptic equations in unbounded domains

Autor: Samuel Nordmann

Publikováno v: Calculus of Variations and Partial Differential Equations
Calculus of Variations and Partial Differential Equations, Springer Verlag, In press

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 e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1e9320d873feaeb3676faaa050a36b07
https://hal.archives-ouvertes.fr/hal-01899477v3/file/HAL_Arxive_Stable_Unbounded.pdf

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