Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds

2015/02/26 by Mastrolia, P., Monticelli, D. D., Punzo, F. · 4 citations
#35K59 #35K92 #35R01 #53C20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.07593

Abstract

We are concerned with nonexistence results of nonnegative weak solutions for a class of quasilinear parabolic problems with a potential on complete noncompact Riemannian manifolds. In particular, we highlight the interplay between the geometry of the underlying manifold, the power nonlinearity and the behavior of the potential at infinity.

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• Liouville type results for semilinear elliptic equation and inequality on pseudo-Hermitian manifolds

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• Nonexistence results for elliptic differential inequalities with a\n potential in bounded domains