𝑝 harmonic measure in simply connected domains revisited
John Lewis · Transactions of the American Mathematical Society · 2014
Let Ω \Omega be a bounded simply connected domain in the complex plane, C \mathbb {C} . Let N N be a neighborhood of ∂ Ω \partial \Omega , let p p be fixed, 1 > p > ∞ , 1 > p > \infty , and let u ^ \hat u be a positive weak solution to the p p Laplace equation in Ω ∩ N . \Omega \cap N. Assume that u ^ \hat u has zero boundary values on ∂ Ω \partial \Omega in the Sobolev sense and extend u ^ \hat u to N ∖ Ω N \setminus \Omega by putting