Nonexistence of variational minimizers related to a quasilinear singular problem in metric measure spaces

preprint2020arXivOpen access

Abstract

In this article we consider a variational problem related to a quasilinear singular problem and obtain a nonexistence result in a metric measure space with a doubling measure and a Poincaré inequality. Our method is purely variational and to the best of our knowledge, this is the first work concerning singular problems in a general metric setting.

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