Eigenfunctions and Harmonic Functions in Convex and Concave Domains
David S Jerison · Birkhäuser Basel eBooks · 1995
Let Ω be a bounded, convex, open subset of R N . This paper concerns the behavior of positive harmonic functions that vanish on ∂Ω. We will consider both the case in which the function is defined in Ω and the case in which the function is defined in the complement of Ω. We will also discuss eigenfunctions defined in Ω. The theme is to study how the shape of Ω influences the size of solutions to these basic elliptic equations.