We extend to the $p=1$ case a measure-theoretic Lemma previously proved by DiBenedetto and Vespri for functions $uin W^{1,p}(K_ ho)$, for $p>1$, where $K_ ho$ is an $N$-dimensional cube of edge $ ho$. It states that if the set where $u$ is bounded away from zero occupies a sizeable portion of $K_ ho$, then the set where $u$ is positive clusters about at least one point of $K_ ho$.
Local clustering of the non-zero set of functions in W^(1,1)(E) / E. DI BENEDETTO ; U. GIANAZZA ; V. VESPRI.. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 17:(2006), pp. 223-225. [10.4171/RLM/465]
Local clustering of the non-zero set of functions in W^(1,1)(E)
VESPRI, VINCENZO
2006
Abstract
We extend to the $p=1$ case a measure-theoretic Lemma previously proved by DiBenedetto and Vespri for functions $uin W^{1,p}(K_ ho)$, for $p>1$, where $K_ ho$ is an $N$-dimensional cube of edge $ ho$. It states that if the set where $u$ is bounded away from zero occupies a sizeable portion of $K_ ho$, then the set where $u$ is positive clusters about at least one point of $K_ ho$.File | Dimensione | Formato | |
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