Phase Space Analysis of Partial Differential Equations

# A strong uniqueness theorem for planar vector fields

speaker: Jorge Guillerme Hounie (Universidade Federal de São Carlos)

abstract: Let L be a locally integrable planar vector field. The strong uniqueness property implies that if u is a solution of Lu=0 for y>0 and its boundary value u(x,0) vanishes on a set o positive measure or has a zero of exponential order it must vanish identically in a neighborhood of {y=0}. The main example of vector with this uniqueness property is the Cauchy-Riemann vector field. We characterize geometrically the locally integrable planar vector fields that possess the strong uniqueness property. A result on pointwise convergence to the boundary value is also given for bounded solutions.

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