Self-similar transformation reduces the Hardy-Sobolev heat equation to an elliptic problem; variational methods give infinitely many subcritical solutions and existence in the critical case, with nonexistence via Pohozaev identity under certain conditions.
Ikeda, C ´esar J
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Variational problems related to self-similar solutions of Hardy-Sobolev heat equation in RN
Self-similar transformation reduces the Hardy-Sobolev heat equation to an elliptic problem; variational methods give infinitely many subcritical solutions and existence in the critical case, with nonexistence via Pohozaev identity under certain conditions.