One-dimensionality of Solutions of Semilinear Elliptic Problems in Cylindrical Domains
Friedemann Brock · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2000
Let be a bounded domain in ℝ with smooth boundary, ℝ, and let satisfy and in , on and on , where ℝ is nondecreasing, if and is continuous and nondecreasing in . Using a rearrangement inequality, we prove that is a function of only.