Calculus of Variations and Geometric Measure Theory

D. Castorina - G. Catino - C. Mantegazza

A Triviality Result for Semilinear Parabolic Equations

created by root on 15 Jul 2020
modified on 23 Jan 2022


Published Paper

Inserted: 15 jul 2020
Last Updated: 23 jan 2022

Journal: Math. Engineering
Volume: 4
Number: 1
Pages: Paper n.002, 15 pp.
Year: 2022


We show a triviality result for “pointwise” monotone in time, bounded “eternal” solutions of the semilinear heat equation $u_t=∆u+
on complete Riemannian manifolds of dimension $n\geq5$ with nonnegative Ricci tensor, when $p$ is smaller than the critical Sobolev exponent $\frac{n+2}{n−2}$.