Infinite dimension of solutions of the Dirichlet problem

Abstract

It is proved that the space of solutions of the Dirichlet problem for the harmonic functions in the unit disk with nontangential boundary limits 0 a.e. has the infinite dimension.

Keywords

• dirichlet problem
• harmonic functions
• laplace equation
• riemann-hilbert problem
• 31a05, 31a20, 31a25, 31b25, 35q15, 30e25, 31c05, 34m50, 35f45