The boundedness of stable solutions to semilinear elliptic equations with linear lower bound on nonlinearities

2023/03/09 by Peng, Fa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2303.05310

Abstract

Let 2≤ n≤9. Suppose that f:R→ R is locally Lipschitz function satisfying f(t)≥ Amin\0,t\-K for all t∈ R with some constant A≥0 and K≥ 0. We establish an a priori interior Hölder regularity of C²-stable solution to the semilinear elliptic equation -Δu=f(u). If, in addition, f is nondecreasing and convex, we obtain the interior Hölder regularity of W^1,2-stable solutions. Note that the dimension n≤9 is optimal.

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