On the Stability of Solutions of Semilinear Elliptic Equations with Robin Boundary Conditions on Riemannian Manifolds

DOI10.1137/15M102647XzbMath1338.35175arXiv1507.06876WikidataQ115246967 ScholiaQ115246967MaRDI QIDQ3460263

Catherine Bandle, Fabio Punzo, Paolo Mastrolia, Dario Daniele Monticelli

Publication date: 7 January 2016

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1507.06876

zbMATH Keywords

stabilitysemilinear elliptic equationsRobin boundary conditions

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Elliptic equations on manifolds, general theory (58J05) Boundary value problems on manifolds (58J32) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Semilinear elliptic equations (35J61) Semilinear parabolic equations (35K58) Pattern formations in context of PDEs (35B36)

Related Items (11)

The Destabilizing Effect of Unbalanced Reaction as Diffusivity Decreases on Reaction-Diffusion Equations in Boundaryless Surfaces ⋮ Rigidity results in diffusion Markov triples ⋮ Reaction-Diffusion Problems on Time-Dependent Riemannian Manifolds: Stability of Periodic Solutions ⋮ Absence of nonnegative solutions to the system of differential inequalities on manifolds ⋮ Classification of stable solutions for boundary value problems with nonlinear boundary conditions on Riemannian manifolds with nonnegative Ricci curvature ⋮ Non-existence of patterns for a class of weighted degenerate operators ⋮ Classification and non-existence results for weak solutions to quasilinear elliptic equations with Neumann or Robin boundary conditions ⋮ New eigenvalue estimates involving Bessel functions ⋮ Non-existence of patterns and gradient estimates in semilinear elliptic equations with Neumann boundary conditions ⋮ Stability results for a reaction-diffusion problem with mixed boundary conditions and applications to some symmetric cases ⋮ Fast diffusion on noncompact manifolds: Well-posedness theory and connections with semilinear elliptic equations

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