Regularity of a Free Boundary with Application to the Pompeiu Problem
Regularity of a Free Boundary with Application to the Pompeiu Problem
In the unit ball B(0, 1), let u and Ω (a domain in R N ) solve the following overdetermined problem:where χ Ω denotes the characteristic function, and the equation is satisfied in the sense of distributions.If the complement of Ω does not develop cusp singularities at the origin then …