A Two Phase Free Boundary Problem Related to Quadrature Domains

作者：Emamizadeh Behrouz; Prajapat Jyotshana V; Shahgholian Henrik^*

来源：Potential Analysis, 2011, 34(2): 119-138.

DOI：10.1007/s11118-010-9184-y

• Free boundary
• Two phase
• Quadrature domains

In this paper we introduce a two phase version of the well-known Quadrature Domain theory, which is a generalized (sub)mean value property for (sub)harmonic functions. In concrete terms, and after reformulation into its PDE version the problem boils down to finding solution to
-Delta u=(mu(+)-lambda(+))(chi{u>0}) - (mu(-) - lambda(-))(chi{u<0}) in IR(N).
where lambda(+/-) >0 are given constants and mu(+/-), are non-negative bounded Radon measures, with compact support. Our primary concern is to discuss existence and geometric properties of solutions.

• 出版日期2011-2