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- W2950711891 abstract "A suitable notion of hypercontractivity for a nonlinear semigroup ${T_t}$ is shown to imply Gagliardo--Nirenberg inequalities for its generator $H$, provided a subhomogeneity property holds for the energy functional $(u,Hu)$. We use this fact to prove that, for semigroups generated by operators of $p$--Laplacian--type, hypercontractivity implies ultracontractivity. We then introduce the notion of subordinated nonlinear semigroups when the corresponding Bernstein function is $f(x)=x^alpha$, and write down an explicit formula for the associated generator. It is shown that, in certain cases, hypercontractivity still holds for the subordinated semigroup and, hence, that Nash--type inequalities holds as well for the subordinated generator." @default.
- W2950711891 created "2019-06-27" @default.
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- W2950711891 date "2007-04-26" @default.
- W2950711891 modified "2023-09-27" @default.
- W2950711891 title "Hypercontractivity, Nash inequalities, and subordination for classes of nonlinear semigroups" @default.
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