On the singular equation ?(u)t=?u

DiBenedetto, Emmanuele; Vespri, Vincenzo

doi:10.1007/bf00382749

Cited by 76 publications

(72 citation statements)

References 7 publications

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“…The proof is quite similar to the one of appendix A.1 of ( [3]) to which we refer the reader for more details. For sake of semplicity we will use the same notation of ( [3]).…”

Section: Proof Of the Lemma 11 When N =mentioning

confidence: 75%

“…Such kind of result has natural application in regularity theory for solutions to PDE's (see for instance the monography ( [2]) for an overview). The first time it was proved in the Appendix of ( [3]) in the case of W 1,p (E). It was generalized in the case of…”

Section: Introductionmentioning

confidence: 95%

“…Here we combine the proofs of ( [3]) and ( [1]) in order to generalize this result in BV spaces. Moreover in this note we use a proof based only on 1-dimensional Poincaré inequality.…”

Section: Introductionmentioning

confidence: 98%

See 2 more Smart Citations

A Quantitative Lusin Theorem for Functions in BV

Telcs

Vespri

2015

Geometric Methods in PDE’s

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We extend to the BV case a measure theoretic lemma previously proved by DiBenedetto, Gianazza and Vespriloc . It states that if the set where u is positive occupies a sizable portion of a open set E then the set where u is positive clusters about at least one point of E. In this note we follow the proof given in the Appendix of [3] so we are able to use only a 1−dimensional Poincaré inequality.

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“…The proof is quite similar to the one of appendix A.1 of ( [3]) to which we refer the reader for more details. For sake of semplicity we will use the same notation of ( [3]).…”

Section: Proof Of the Lemma 11 When N =mentioning

confidence: 75%

Section: Introductionmentioning

confidence: 95%

See 1 more Smart Citation

A Quantitative Lusin Theorem for Functions in BV

Telcs

Vespri

2015

Geometric Methods in PDE’s

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“…The Lemma was established in [1] for u ∈ W 1,p (K ρ ) and p > 1. Such a limitation on p was essential to the proof.…”

Section: Introduction and Statement Of The Resultsmentioning

confidence: 99%

Local clustering of the non-zero set of functions in $W^{1,1}(E)$

DiBenedetto¹,

Gianazza²,

Vespri³

2006

Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur.

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Mathematical analysis. -Local clustering of the non-zero set of functions in W 1,1 (E), by EMMANUELE DIBENEDETTO, UGO GIANAZZA and VINCENZO VESPRI.ABSTRACT. -We extend to the p = 1 case a measure-theoretic lemma previously proved by DiBenedetto and Vespri for functions u ∈ W 1,p (K ρ ) where K ρ is an N -dimensional cube of edge ρ. It states that if the set where u is bounded away from zero occupies a sizeable portion of K ρ , then the set where u is positive clusters about at least one point of K ρ .

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“…If G(u) is degenerate on an interval, for instance the two-phase Stefan problem, the continuity of G(u) was first proved in [3], and the Hölder continuity of G (u) with an implicit Hölder exponent was obtained in [6]. Some special cases for G(u) having a degenerate interval were also studied in [13].…”

mentioning

confidence: 99%

Hölder estimates of solutions to a degenerate diffusion equation

2001

Proc. Amer. Math. Soc.

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On the singular equation ?(u)t=?u

Cited by 76 publications

References 7 publications

A Quantitative Lusin Theorem for Functions in BV

A Quantitative Lusin Theorem for Functions in BV

Local clustering of the non-zero set of functions in $W^{1,1}(E)$

Hölder estimates of solutions to a degenerate diffusion equation

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