In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem −∆u = f(x, y) finding a geometric condition involving the curvature of the boundary and the normal derivative of f on the boundary to ensure uniqueness of the critical point. In the second part we consider stable solutions of the nonlinear problem −∆u = f(u) in perturbation of convex domains.
Battaglia, L., De Regibus, F., Grossi, M. (2024). ON THE SHAPE OF SOLUTIONS TO ELLIPTIC EQUATIONS IN POSSIBLY NON CONVEX PLANAR DOMAINS. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 17(4), 1588-1598 [10.3934/dcdss.2023194].
ON THE SHAPE OF SOLUTIONS TO ELLIPTIC EQUATIONS IN POSSIBLY NON CONVEX PLANAR DOMAINS
Battaglia L.;Grossi M.
2024-01-01
Abstract
In this note we prove uniqueness of the critical point for positive solutions of elliptic problems in bounded planar domains: we first examine the Poisson problem −∆u = f(x, y) finding a geometric condition involving the curvature of the boundary and the normal derivative of f on the boundary to ensure uniqueness of the critical point. In the second part we consider stable solutions of the nonlinear problem −∆u = f(u) in perturbation of convex domains.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
