Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature

2024/03/25 by Aryan, Shrey, Law, Michael B.
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.16783

Abstract

We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Langford and Scheuer. To the best of our knowledge, this is the first general concavity principle established on spaces with non-constant sectional curvature.

Related

• Concavity principles for nonautonomous elliptic equations and applications
• Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
• Quantitative and exact concavity principles for parabolic and elliptic equations
• Concavity properties for solutions to p-Laplace equations with concave nonlinearities
• High-order estimates for fully nonlinear equations under weak concavity assumptions