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

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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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Authors and Affiliations

  1. Università degli Studi di Milano, Milan, Italy

    Paolo Mastrolia

  2. Politecnico di Milano, Milan, Italy

    Dario D. Monticelli

  3. Università della Calabria, Rende, CS, Italy

    Fabio Punzo

Authors
  1. Paolo Mastrolia
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  2. Dario D. Monticelli
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  3. Fabio Punzo
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Corresponding author

Correspondence to Fabio Punzo.

Additional information

P. Mastrolia, D. D. Monticelli and F. Punzo are supported by GNAMPA project “Analisi globale ed operatori degeneri” and are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM).

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Mastrolia, P., Monticelli, D.D. & Punzo, F. Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds. Math. Ann. 367, 929–963 (2017). https://doi.org/10.1007/s00208-016-1393-2

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  • DOI: https://doi.org/10.1007/s00208-016-1393-2

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