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We investigate the regularity of semi-stable, radially symmetric, anddecreasing solutions for a class of quasilinear reaction-diffusion equations inthe inhomogeneous context of Riemannian manifolds. We prove uniformboundedness, Lebesgue and Sobolev estimates for this class of solutions forequations involving the p-Laplace Beltrami operator and locally Lipschitznon-linearity. We emphasize that our results do not depend on the boundaryconditions and the specific form of the non-linearities and metric. Moreover,as an application, we establish regularity of the extremal solutions forequations involving the p-Laplace Beltrami operator with zero Dirichletboundary conditions.

Regularity of stable solutions to quasilinear elliptic equations on Riemannian models