Calculus of Variations and Geometric Measure Theory
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D. Castorina - G. Catino - C. Mantegazza

A Triviality Result for Semilinear Parabolic Equations

created by root on 15 Jul 2020
modified on 04 Aug 2021


Accepted Paper

Inserted: 15 jul 2020
Last Updated: 4 aug 2021

Journal: Math. Engineering
Year: 2021


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 $\frac{n+2}{n−2}$.


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