Partial analyticity and nodal sets for nonlinear elliptic systems

Herbert Koch (1) , Nikolai Nadirashvili (2)

1 Rheinische Friedrich-Wilhelms-Universität Bonn
2 I2M - Institut de Mathématiques de Marseille

We study partial analyticity of solutions to elliptic systems and analyticity of level sets of solutions to nonlinear elliptic systems. We consider several applications, including analyticity of flow lines for bounded stationary solutions to the 2-d Euler equation, and analyticity of water waves with and without surface tension.

Mots clés: nonlinear elliptic systems; analyticity; 2-d Euler equation; water waves

Domaines: Equations aux dérivées partielles [math.AP]

Herbert Koch, Nikolai Nadirashvili. Partial analyticity and nodal sets for nonlinear elliptic systems. 2015. ⟨hal-01338320⟩